Dissertations / Theses on the topic 'Finite abelian group'
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Mkiva, Soga Loyiso Tiyo. "The non-cancellation groups of certain groups which are split extensions of a finite abelian group by a finite rank free abelian group." Thesis, University of the Western Cape, 2008. http://etd.uwc.ac.za/index.php?module=etd&action=viewtitle&id=gen8Srv25Nme4_8520_1262644840.
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The groups we consider in this study belong to the class X0 of all finitely generated groups with finite commutator subgroups.
Eyl, Jennifer S. "Spanning subsets of a finite abelian group of order pq /." Electronic version (PDF), 2003. http://dl.uncw.edu/etd/2003/eylj/jennifereyl.pdf.
Full textGiangreco, Maidana Alejandro José. "Cyclic abelian varieties over finite fields." Thesis, Aix-Marseille, 2019. http://www.theses.fr/2019AIXM0316.
Full textThe set A(k) of rational points of an abelian variety A defined over a finite field k forms a finite abelian group. This group is suitable for multiple applications, and its structure is very important. Knowing the possible group structures of A(k) and some statistics is then fundamental. In this thesis, we focus our interest in "cyclic varieties", i.e. abelian varieties defined over finite fields with cyclic group of rational points. Isogenies give us a coarser classification than that given by the isomorphism classes of abelian varieties, but they provide a powerful tool in algebraic geometry. Every isogeny class is determined by its Weil polynomial. We give a criterion to characterize "cyclic isogeny classes", i.e. isogeny classes of abelian varieties defined over finite fields containing only cyclic varieties. This criterion is based on the Weil polynomial of the isogeny class.From this, we give bounds on the fractions of cyclic isogeny classes among certain families of isogeny classes parameterized by their Weil polynomials.Also we give the proportion of "local"-cyclic isogeny classes among the isogeny classes defined over the finite field mathbb{F}_q with q elements, when q tends to infinity
McDonough, Heather Mallie. "Classification of prime ideals in integral group algebras of finite abelian groups." College Park, Md. : University of Maryland, 2005. http://hdl.handle.net/1903/2513.
Full textThesis research directed by: Dept. of Mathematics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
Marseglia, Stefano. "Isomorphism classes of abelian varieties over finite fields." Licentiate thesis, Stockholms universitet, Matematiska institutionen, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-130316.
Full textNgcibi, Sakhile Leonard. "Studies of equivalent fuzzy subgroups of finite abelian p-Groups of rank two and their subgroup lattices." Thesis, Rhodes University, 2006. http://hdl.handle.net/10962/d1005230.
Full textMariani, Alessandro. "Finite-group Yang-Mills lattice gauge theories in the Hamiltonian formalism." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/21183/.
Full textMut, Sagdicoglu Oznur. "On Finite Groups Admitting A Fixed Point Free Abelian Operator Group Whose Order Is A Product Of Three Primes." Phd thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/3/12610990/index.pdf.
Full textDecker, Erin. "On the construction of groups with prescribed properties." Diss., Online access via UMI:, 2008.
Find full textAssis, Ailton Ribeiro de. "Idempotentes em Álgebras de Grupos e Códigos Abelianos Minimais." Universidade Federal da Paraíba, 2011. http://tede.biblioteca.ufpb.br:8080/handle/tede/7401.
Full textCoordenação de Aperfeiçoamento de Pessoal de Nível Superior
In this work, we study the semisimple group algebras FqCn of the finite abelian groups Cn over a finite field Fq and give conditions so that the number of its simple components is minimal; i.e. equal to the number of simple components of the rational group algebra of the same group. Under such conditions, we compute the set of primitive idempotents of FqCn and from there, we study the abelian codes as minimal ideals of the group algebra, which are generated by the primitive idempotents, computing their dimension and minimum distances.
Neste trabalho, estudamos álgebras de grupos semisimples FqCn de grupos abelianos finitos Cn sobre um corpo finito Fq e as condições para que o número de componentes simples seja mínimo, ou seja igual ao número de componentes simples sobre a álgebra de grupos racionais do mesmo grupo. Sob tais condições, calculamos o conjunto de idempotentes primitivos de FqG e a de partir daí, estudamos os códigos cíclicos como ideais minimais da álgebra de grupo, os quais são gerados pelos idempotentes primitivos, calculando suas dimensões e distâncias mínimas.
Albuquerque, Flávio Alves de. "Classificação de Automorfismos de Grupos Finitos." Universidade Federal da Paraíba, 2011. http://tede.biblioteca.ufpb.br:8080/handle/tede/7355.
Full textCoordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
In this paper we study finite Abelian groups, where state and prove the fundamental theorem of finitely generated abelian groups, as well as determine a characterization of automorphisms of a p-group, moreover, we exhibit an algorithm that determines the count of the number of automorphisms of p-groups. Finally, we show the automorphisms of the non-Abelian dihedral group.
Neste trabalho estudamos Grupos Abelianos finitos, onde enunciamos e provamos o Teorema fundamental dos grupos abelianos finitamente gerados, bem como determinamos uma caracterização dos automorfismos de um p-grupo, além disso, exibimos um algoritmo que determina a contagem do número de automorfismos desses p-grupos. Por fim, mostramos os automorfismos do grupo não-Abeliano Diedral .
Silva, Ana Shirley Monteiro da. "Grupos nos quais o conjunto dos comutadores possui cobertura finita por subgrupos cÃclicos." Universidade Federal do CearÃ, 2010. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=5250.
Full textGiven a word w and a group G, suppose that the set can be Gw covered by finite cyclic subgroups. It is true that w(G) can also be covered by finite cyclic subgroups? This dissertation will show that the answer is positive for the word switch.
Krause, Linda J. "Counting the number of automorphisms of finite abelian groups." Virtual Press, 1994. http://liblink.bsu.edu/uhtbin/catkey/917027.
Full textDepartment of Mathematical Sciences
Beltrán, Antonio, María José Felipe, Gunter Malle, Alexander Moretó, Gabriel Navarro, Lucia Sanus, Ronald Solomon, and Pham Huu Tiep. "Nilpotent and abelian Hall subgroups in finite groups." AMER MATHEMATICAL SOC, 2015. http://hdl.handle.net/10150/614976.
Full textBarker, Russell. "L#kappa#-equivalence and Hanf functions for finite structures." Thesis, University of Oxford, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.270249.
Full textNickodemus, M. H. "Natural dualities for finite groups with abelian Sylow subgroups." Connect to online resource, 2007. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3273669.
Full textOkay, Cihan. "Homotopy colimits of classifying spaces of finite abelian groups." Thesis, University of British Columbia, 2014. http://hdl.handle.net/2429/46380.
Full textLim, Junghwan. "Galois actions on non-abelian finite groups and applications." Thesis, University of Oxford, 2017. http://ora.ox.ac.uk/objects/uuid:c8ef61d6-ddd0-46eb-9304-1ab091b60f35.
Full textKazaz, Mustafa. "Finite groups and coverings of surfaces." Thesis, University of Southampton, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.264739.
Full textNgcibi, Sakhile L. "Case studies of equivalent fuzzy subgroups of finite abelian groups." Thesis, Rhodes University, 2002. http://hdl.handle.net/10962/d1005215.
Full textCosta, Carlos Henrique Alves. "Automorfismos de Grupos Abelianos Finitos." Universidade Federal de Viçosa, 2014. http://locus.ufv.br/handle/123456789/4930.
Full textCoordenação de Aperfeiçoamento de Pessoal de Nível Superior
The set of all automorphisms of a group G form a group denoted by Aut(G). In this work we study automorphisms of finite abelian groups, mainly following the approach by Christopher J. Hillar and Darren L. Rhea according to the paper Automorphisms of finite abelian Groups (American Mathematical Monthly 114 n. 10 (2007) 917-923). The main objective is to characterize the automorphism group Aut(G), where G is a finite abelian group and present a formula for the number of elements of Aut(G). The determination of this formula is done in two distinct ways: one from the calculation of the number of elements of the group Aut(G) viewed as the group of units of the endomorphisms ring End(G) and the other using certain characteristic subgroups of the group G. This latter method follows the development made by Heinrich Kuhn in his doctoral thesis.
O conjunto de todos os automorfismos de um grupo G forma um grupo denotado por Aut(G). Neste trabalho estudamos automorfismos de grupos abelianos finitos, seguindo principalmente a abordagem feita por Christopher J. Hillar e Darren L. Rhea no artigo Automorphisms of finite abelian Groups (American Mathematical Monthly 114 n. 10 (2007) 917-923). O objetivo principal ́e fazer uma caracterização do grupo de automorfismos Aut(G), onde G ́e um grupo abeliano finito e apresentar uma fórmula para o número de elementos de Aut(G). A determinação desta f ́ormula ́e feita de duas maneiras distintas: uma a partir do cálculo do número de elementos do grupo Aut(G) visto como grupo das unidades do anel de endomorfismos End(G) e a outra utilizando certos subgrupos característicos do grupo G. Esse último método segue o desenvolvimento feito por Heinrich Kuhn, em sua tese de doutorado.
Callegaro, Filippo. "Cohomology of finite and affine type Artin groups over Abelian representation /." Pisa, Italy : Edizioni della normale, 2009. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=017728632&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.
Full textKadets, Borys. "Arboreal representations, sectional monodromy groups, and abelian varieties over finite fields." Thesis, Massachusetts Institute of Technology, 2020. https://hdl.handle.net/1721.1/126927.
Full textCataloged from the official PDF of thesis.
Includes bibliographical references (pages 93-97).
This thesis consists of three independent parts. The first part studies arboreal representations of Galois groups - an arithmetic dynamics analogue of Tate modules - and proves some large image results, in particular confirming a conjecture of Odoni. Given a field K, a separable polynomial [mathematical expression], and an element [mathematical expression], the full backward orbit [mathematical expression] has a natural action of the Galois group [mathematical expression]. For a fixed [mathematical expression] with [mathematical expression] and for most choices of t, the orbit [mathematical expression] has the structure of complete rooted [mathematical expression]. The Galois action on [mathematical expression] thus defines a homomorphism [mathematical expression]. The map [mathematical expression] is the arboreal representation attached to f and t.
In analogy with Serre's open image theorem, one expects [mathematical expression] to hold for most f, t, but until very recently for most degrees d not a single example of a degree d polynomial [mathematical expression] with surjective [mathematical expression],t was known. Among other results, we construct such examples in all sufficiently large even degrees. The second part concerns monodromy of hyperplane section of curves. Given a geometrically integral proper curve [mathematical expression], consider the generic hyperplane [mathematical expression]. The intersection [mathematical expression] is the spectrum of a finite separable field extension [mathematical expression] of degree [mathematical expression]. The Galois group [mathematical expression] is known as the sectional monodromy group of X. When char K = 0, the group [mathematical expression] equals [mathematical expression] for all curves X.
This result has numerous applications in algebraic geometry, in particular to the degree-genus problem. However, when char K > 0, the sectional monodromy groups can be smaller. We classify all nonstrange nondegenerate curves [mathematical expression], for [mathematical expression] such that [mathematical expression]. Using similar methods we also completely classify Galois group of generic trinomials, a problem studied previously by Abhyankar, Cohen, Smith, and Uchida. In part three of the thesis we derive bounds for the number of [mathematical expression]-points on simple abelian varieties over finite fields; these improve upon the Weil bounds. For example, when q = 3, 4 the Weil bound gives [ .. ] for all abelian varieties A. We prove that [mathematical expression], [mathematical expression] hold for all but finitely many simple abelian varieties A (with an explicit list of exceptions).
by Borys Kadets.
Ph. D.
Ph.D. Massachusetts Institute of Technology, Department of Mathematics
Appiah, Isaac Kwadwo. "The classsification of fuzzy subgroups of some finite Abelian p-groups of rank 3." Thesis, University of Fort Hare, 2016. http://hdl.handle.net/10353/2468.
Full textKuivinen, Fredrik. "Tight Approximability Results for the Maximum Solution Equation Problem over Abelian Groups." Thesis, Linköping University, Department of Computer and Information Science, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-3240.
Full textIn the maximum solution equation problem a collection of equations are given over some algebraic structure. The objective is to find an assignment to the variables in the equations such that all equations are satisfied and the sum of the variables is maximised. We give tight approximability results for the maximum solution equation problem when the equations are given over finite abelian groups. We also prove that the weighted and unweighted versions of this problem have asymptotically equal approximability thresholds.
Furthermore, we show that the problem is equally hard to solve as the general problem even if each equation is restricted to contain at most three variables and solvable in polynomial time if the equations are restricted to contain at most two variables each. All of our results also hold for the generalised version of maximum solution equation where the elements of the group are mapped arbitrarily to non-negative integers in the objective function.
Morotti, Lucia [Verfasser]. "Explicit construction of universal sampling sets for finite abelian and symmetric groups / Lucia Morotti." Aachen : Hochschulbibliothek der Rheinisch-Westfälischen Technischen Hochschule Aachen, 2014. http://d-nb.info/1059630214/34.
Full textWakefield, Thomas Philip. "Verifying Huppert's Conjecture for the simple groups of Lie type of rank two." [Kent, Ohio] : Kent State University, 2008. http://etd.ohiolink.edu/etd/send-pdf.cgi/Wakefield%20Thomas%20Philip.pdf?acc_num=kent1211880668.
Full textTitle from PDF t.p. (viewed Sept. 17, 2009). Advisor: Donald White. Keywords: Huppert's Conjecture; character degrees; nonabelian finite simple groups Includes bibliographical references (p. 103-105).
Viehweg, Jarom. "Ore's theorem." CSUSB ScholarWorks, 2011. https://scholarworks.lib.csusb.edu/etd-project/145.
Full textSiegemeyer, Christian [Verfasser], and Michael [Akademischer Betreuer] Joachim. "On the Gromov-Lawson-Rosenberg conjecture for finite abelian 2-groups of rank 2 / Christian Siegemeyer. Betreuer: Michael Joachim." Münster : Universitäts- und Landesbibliothek der Westfälischen Wilhelms-Universität, 2013. http://d-nb.info/1031885560/34.
Full textFiedler, Leander Karl Wilhelm [Verfasser]. "Haag duality and Jones-Kosaki-Longo index in Kitaev's quantum double models for finite abelian groups / Leander Karl Wilhelm Fiedler." Hannover : Technische Informationsbibliothek (TIB), 2017. http://d-nb.info/1136090622/34.
Full textNuez, González Javier de la [Verfasser], and Katrin [Akademischer Betreuer] Tent. "On expansions of non-abelian free groups by cosets of a finite index subgroup / Javier de la Nuez González ; Betreuer: Katrin Tent." Münster : Universitäts- und Landesbibliothek Münster, 2016. http://d-nb.info/114190764X/34.
Full textLumia, Luca. "Digital quantum simulations of Yang-Mills lattice gauge theories." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/22355/.
Full textCôme, Rémi. "Analyse sur les espaces singuliers et théorie de l’indice." Electronic Thesis or Diss., Université de Lorraine, 2020. http://www.theses.fr/2020LORR0096.
Full textThis thesis is set in the general context of extending the theory of elliptic operators, well-understood in the smooth setting, to so-called singular domains. The methods used rely on operator algebras and tools coming from non commutative geometry, together with suitable pseudodifferential calculi that are often built from a groupoid adapted to the particular geometry of the problem. The first part of the thesis deals with the general investigation of a particular class of such groupoids, called Fredholm, that provide a very good setting for the study of elliptic operators. One of the major results proved here is that this Fredholm property is local, in the sense that it only depends on the restrictions of the groupoid to sufficiently many open subsets. In the same spirit, we study with C. Carvalho and Y. Qiao groupoids whose local structure is given by gluing group actions, and consider in particular a groupoid suited to the study of layer potential operators. This part concludes with a well-posedness result for a boundary value problem on a domain with a rotational cusp. The second part deals with equivariant operators on a compact manifold, acted upon by a finite group. We answer the following question: given an irreducible representation of the group, under which condition is a differential operator Fredholm between the corresponding isotypical components of the Sobolev spaces? In a joint work with A. Baldare, M. Lesch and V. Nistor, we introduce a corresponding notion of ellipticity associated with some fixed irreducible representation, and show that it characterizes Fredholm operators
楊蕙芝. "Finite rank torsion free abelian group." Thesis, 1990. http://ndltd.ncl.edu.tw/handle/68494763600973477471.
Full textRoberts, Collin Donald. "The Cohomology Ring of a Finite Abelian Group." Thesis, 2013. http://hdl.handle.net/10012/7276.
Full textChen, Yung-Chain, and 陳永清. "On Hom Of Finite Rank Torsion Free Abelian Group." Thesis, 1993. http://ndltd.ncl.edu.tw/handle/87646784711705670555.
Full text淡江大學
數學系
81
We wanted to understand the structure of finite rankorsion free abelian group. But in fact, there are only few restricted torsion free abelian groups that resulted in good conclusion. In this paper, we describe about hom of finite rank torsion free abelian groups and classify them by types. In generally, the type of group desides the part of structure of it. This paper has two parts. The first part contains 3 lemmas, 4 theorems and 2 corollaries, the important results of it are theorem,8 and corollary,9. Theorem,8 : Suppose that A and B are torsion free groups of rank-1. (a) If type(A)$\le$type(B) then Hom(A,B) is a rank-1 torsion free groups with type=[($k_p$)], where 0$\ne a\in A$, $0\ne b\in B$, $h^A(a)=(k_p)\le h^B(b)=( l_p), m_p=\infty$ if $l_p= \infty ,and m_p=l_p - k_p if l_p is finite. (b) If type(A) =[(k_p)] then type(Hom(A,A))=[(m_p)] is non-nil, where m_p= \infty if k_p=\infty and m_p=0 if k_p= \infty. Corollary,9 : Assume A is a tosion free group of rank-1. The fllowing are equivalent : (a) A have non-nil type ; (b) type(A)+type(A)=ype(A); (c) A\congHom(A,A); (d) A is isomorphic to the additive group of a subring of Q; (e) If 0\ne a\in A then A/Za=T\oplusD, where T is a finite torsion group and D\cong \oplus_p\in S Z(p^\infty) for some subset S of \Pi. The second part contains 2 lemmas, 5 theorems and 2 corollaries, the important conclusion of it are theorem,15 and corollary,17, 18.
Ibrahim, Caroline Maher Boulis Heil Wolfgang. "Finite abelian group actions on orientable circle bundles over surfaces." 2004. http://etd.lib.fsu.edu/theses/available/etd-07122004-135529.
Full textAdvisor: Dr. Wolfgang Heil, Florida State University, College of Arts and Sciences, Dept. of Mathematics. Title and description from dissertation home page (viewed Sept. 28, 2004). Includes bibliographical references.
Then, Tsai Mei, and 蔡美珍. "On tonsor product of finite rank torsion free abelian group." Thesis, 1993. http://ndltd.ncl.edu.tw/handle/20414803127362939112.
Full text淡江大學
數學系
81
Suppose that R is a ring,A is a right R-module and B is a left R-module then $A\otimes_Z B$ is define to be F/N where F is the free abelian group with elements of $A \otimes_Z B$ as a basie. If anabelian group has all its elements of finite order,we shall call it a torsion group. The other extreme case is that where all the elements have infinite order,we then call the group torsion free.Define rank(A)=$dim_Q (Q\otimes_Z A)$;p-rank( A)=$dim_Q(A/pA)$ and $Z_p={m/n in Q |gcd(n,p)=1}$,the localization of Z at p.If A is a torsion free abelian group of finite rank and n is non-nil in Z,hten A/nA is finite.Moreover, p-rank(A)$\le$ rank(A),where p is prime. We define the p-height of a in A,height sequence and call an equivalence class of height sequence a type.Then we get some results:Suppose A and B are rank-1 torsion free en (1) A and B are isomorphic iff type( A)=type(B); (2) $A\otimes_Z B$ is a torsion free group of rank-1 with type$(\otimes_Z B)$=type(A)+type(B);(3) $A\otimes_Z A$ and $B\otimes_Z B$ are isomorphic iff A and B are isomorphic ; (4) type(C)=[($m_p$)], $m_p\le \infty $ iff $A\otimes_Z C$ and $B\otimes_Z C$ are isomorphic then A and B are isomorphic. Finally,we define non-nil type and R(A)-locally free, where A is a torsion free group of rank-1.The following arelent:(a) A has non-nil type. (b) type(A)+type(A)=type (A). (c) $A\otimes_Z A$ and A are isomsrphic.Let A be torsionof finite rank and A=$ Z_p \otimes_Z A $, then A is R(A)- lacally free iff A is a free $Z_p$-module for each p with pA$\ne $A,and so on.
Chi, Chih-Tsung, and 紀志聰. "On finite covering over abelian varieties and invariant of finite subgroup of Heisenberg group." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/04149075872779760012.
Full text國立中正大學
數學研究所
92
We produce some finite covering over abelian variables by explicit construction. This is done by computing invariants of finite heisenberg group. We have done this for coving of degree 3 and 4, which corresponding to Heisenberg group action on 2 and 3 variables.
Vipismakul, Wasin. "The stabilizer of the group determinant and bounds for Lehmer's conjecture on finite abelian groups." 2013. http://hdl.handle.net/2152/21685.
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Seretlo, Thekiso Trevor. "Fischer Clifford matrices and character tables of certain groups associated with simple groups O+10(2) [the simple orthogonal group of dimension 10 over GF (2)], HS and Ly." Thesis, 2011. http://hdl.handle.net/10413/9378.
Full textThesis (Ph.D.)-University of KwaZulu-Natal, Pietermaritzburg, 2011.
Lee, Ying-Chiao, and 李盈嬌. "The Automorphism Groups of Finite Abelian Groups." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/30768082347116360513.
Full text國立臺灣大學
數學研究所
91
Abstract The discussions in this thesis are focus on the p-structure of the Aut(G) of finite abelian group G. In the §1, we introduce some existing conclusions relative to this topic. In the §2, we show the basic results for the beginning of our discussions. And then in the §3 and §4, we give the generators and relations of the Sylow p-subgroup P of Aut(G). In the §6, we describe the center of P and then we describe the commutator subgroup of P in the §7. In the §8, we try to classify the conjugacy classes of P for the cases that P is included in GL2(Z/p2Z) and P is included in GL2(Z/p3Z). In the relations given in the §3 and §4, we also need to find a number hn,l such that (1 + p)hn,l congruent to 1 + pl (mod pn) for given n,l. Thus in the §5, we discuss the problem of how to find such number hn,l.
Chang, Chih-Ming, and 張世明. "Character Tables of Finite Abelian Groups." Thesis, 1997. http://ndltd.ncl.edu.tw/handle/88314262552198207920.
Full text逢甲大學
應用數學研究所
85
The main purpose of this thesis is to introduce elementary properties of group representations and group characters including Maschke's theorem, orthogonality relations, and Burnside's theorem. Finally in the main theorems we adopted thepaper from L. Solomon which provided us an inequality governing the sum of the elements in the character table and we proved that the character table of a finite group is symmetric if and only if the group is abelian.
Naymie, Cassandra. "Generalisations of Roth's theorem on finite abelian groups." Thesis, 2012. http://hdl.handle.net/10012/7162.
Full textWang, Sheng Yuan, and 王聖淵. "On pure Subgroups of finite rank torsion free completely decomposable abelian groups." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/68102544275448645800.
Full text淡江大學
數學學系
89
R. Baer, in 1937, gave a complete set of invariants for finite rank completely decomposable groups. After such a promising start, the theory of the structure of finite rank torsion groups has become stagnant. One of the difficulties has been the absence of a suitable intermediate class of groups, i.e. a class large enough to contain interesting examples, small enough that there is some hope of understanding the structure of groups in the class, and admitting enough different characterizations to provide a variety of techniques and reasonable problems. The class of pure subgroups of finite rank completely decomposable groups plays an important role in the theory of finite rank torsion free abelian groups. The class was first presented by M.C.R Butler in 1965 and then named after him by Lady. This class of Butler groups contains all completely decomposable groups. In the thesis, we will examine the structure of Butler groups. Butler proved that a torsion free group is a pure subgroup of a finite rank completely decomposable group if and only if it is the homomorphic image of a finite rank completely decomposable group. He also gave a characterization of these groups in term of types and their associated fully invariant subgroups. In [6], Lady introduced the concept of a regulating subgroup of an almost completely decomposable group, which turned out to be a completely decomposable subgroup of minimal index. The notation of regulating subgroups is generalized to the class of Butler groups. David M. Arnold, in 1981, defined the groups of B0-groups and B1-groups. If a Butler group is a B0-group, then it is a unique regulating subgroup of itself. If a Butler group is a B1-group then each regulating subgroup of it is a B0-groups. Hence, the concept of regulating subgroups plays an important role to examine the structures of Butler groups. In chapter 4, we will give the relations and properties between these groups in terms of regulating subgroups.
Friedenberg, Stefan [Verfasser]. "Torsion free extensions of torsion free abelian groups of finite rank / von Stefan Friedenberg." 2009. http://d-nb.info/1001679725/34.
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