Relevant bibliographies by topics / Free abelian group

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Free abelian group'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Free abelian group"

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Dikranjan, Dikran, Anna Giordano Bruno, and Dmitri Shakhmatov. "Minimal pseudocompact group topologies on free abelian groups." Topology and its Applications 156, no. 12 (2009): 2039–53. http://dx.doi.org/10.1016/j.topol.2009.03.028.

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Bastos, Gervasio G., and T. M. Viswanathan. "Torsion-free Abelian Groups, Valuations and Twisted Group Rings." Canadian Mathematical Bulletin 31, no. 2 (1988): 139–46. http://dx.doi.org/10.4153/cmb-1988-021-x.

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AbstractAnderson and Ohm have introduced valuations of monoid rings k[Γ] where k is a field and Γ a cancellative torsion-free commutative monoid. We study the residue class fields in question and solve a problem concerning the pure transcendence of the residue fields.
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Katz, E., S. A. Morris, and P. Nickolas. "Free subgroups of free abelian topological groups." Mathematical Proceedings of the Cambridge Philosophical Society 100, no. 2 (1986): 347–53. http://dx.doi.org/10.1017/s0305004100077343.

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In this paper we prove a theorem which gives general conditions under which the free abelian topological group F(Y) on a space Y can be embedded in the free abeian topological group F(X) on a space X.
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NISHINAKA, TSUNEKAZU. "GROUP RINGS OF COUNTABLE NON-ABELIAN LOCALLY FREE GROUPS ARE PRIMITIVE." International Journal of Algebra and Computation 21, no. 03 (2011): 409–31. http://dx.doi.org/10.1142/s0218196711006273.

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We prove that every group ring of a non-abelian locally free group which is the union of an ascending sequence of free groups is primitive. In particular, every group ring of a countable non-abelian locally free group is primitive. In addition, by making use of the result, we give a necessary and sufficient condition for group rings of ascending HNN extensions of free groups to be primitive, which extends the main result in [Group rings of proper ascending HNN extensions of countably infinite free groups are primitive, J. Algebra317 (2007) 581–592] to the general cardinality case.
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Morris, Sidney A., and Vladimir G. Pestov. "Open subgroups of free abelian topological groups." Mathematical Proceedings of the Cambridge Philosophical Society 114, no. 3 (1993): 439–42. http://dx.doi.org/10.1017/s0305004100071723.

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We prove that any open subgroup of the free abelian topological group on a completely regular space is a free abelian topological group. Moreover, the free topological bases of both groups have the same covering dimension. The prehistory of this result is as follows. The celebrated Nielsen–Schreier theorem states that every subgroup of a free group is free, and it is equally well known that every subgroup of a free abelian group is free abelian. The analogous result is not true for free (abelian) topological groups [1,5]. However, there exist certain sufficient conditions for a subgroup of a f
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Johnson, F. E. A. "Stably free cancellation for abelian group rings." Archiv der Mathematik 102, no. 1 (2014): 7–10. http://dx.doi.org/10.1007/s00013-013-0599-8.

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Zastrow, Andreas. "The Non-abelian Specker-Group Is Free." Journal of Algebra 229, no. 1 (2000): 55–85. http://dx.doi.org/10.1006/jabr.1999.8261.

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Brunker, Don, та Denis Higgs. "Constructions of Σ-groups, relatively free Σ-groups". Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 46, № 1 (1989): 8–21. http://dx.doi.org/10.1017/s1446788700030354.

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AbstractA Σ-group is an abelian group on which is given a family of infinite sums having properties suggested by, but weaker than, those which hold for absolutely convergent series of real or complex numbers. Two closely related questions are considered. The first concerns the construction of a Σ-group from an arbitrary abelian group on which certain series are given to be summable, certain of these series being required to sum to zero. This leads to a Σ-theoretic construction of R from Q and in general of the completion of an arbitrary metrizable abelian group (with the associated uncondition
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Tkačenko, Michael G., and Luis M. Villegas-Silva. "Refining connected topological group topologies on Abelian torsion-free groups." Journal of Pure and Applied Algebra 124, no. 1-3 (1998): 281–88. http://dx.doi.org/10.1016/s0022-4049(96)00109-0.

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FATICONI, THEODORE G. "DIAGRAMS OF AN ABELIAN GROUP." Bulletin of the Australian Mathematical Society 80, no. 1 (2009): 38–64. http://dx.doi.org/10.1017/s0004972708001238.

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AbstractIn this paper, we characterize quadratic number fields possessing unique factorization in terms of the power cancellation property of torsion-free rank-two abelian groups, in terms of Σ-unique decomposition, in terms of a pair of point set topological properties of Eilenberg–Mac Lane spaces, and in terms of the sequence of rational primes. We give a complete set of topological invariants of abelian groups, we characterize those abelian groups that have the power cancellation property in the category of abelian groups, and we characterize those abelian groups that have Σ-unique decompos
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Dissertations / Theses on the topic "Free 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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<p>&nbsp<br></p> <p align="left">The groups we consider in this study belong to the class <font face="F30">X</font><font face="F25" size="1"><font face="F25" size="1">0 </font></font><font face="F15">of all finitely generated groups with finite commutator subgroups.</font></p>
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Dexter, Cache Porter. "Schur Rings over Infinite Groups." BYU ScholarsArchive, 2019. https://scholarsarchive.byu.edu/etd/8831.

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A Schur ring is a subring of the group algebra with a basis that is formed by a partition of the group. These subrings were initially used to study finite permutation groups, and classifications of Schur rings over various finite groups have been studied. Here we investigate Schur rings over various infinite groups, including free groups. We classify Schur rings over the infinite cyclic group.
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Mut, 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.

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A long-standing conjecture states that if A is a finite group acting fixed point freely on a finite solvable group G of order coprime to jAj, then the Fitting length of G is bounded by the length of the longest chain of subgroups of A. If A is nilpotent, it is expected that the conjecture is true without the coprimeness condition. We prove that the conjecture without the coprimeness condition is true when A is a cyclic group whose order is a product of three primes which are coprime to 6 and the Sylow 2-subgroups of G are abelian. We also prove that the conjecture without the coprimeness condi
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Alexandrou, Maria. "Free centre-by-(abelian-by-exponent 2) groups." Thesis, University of Manchester, 2014. https://www.research.manchester.ac.uk/portal/en/theses/free-centrebyabelianbyexponent-2-groups(58ddc606-5d9e-4b23-a5cc-05a56cabf2ca).html.

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In the present thesis we study free centre-by-(abelian-by-exponent 2) groups. These are in the class of free centre-by-metabelian groups which in turn are a special case of quotients of the form F=[R0; F] where F is a free group, R is a normal subgroup of F and R0 is the commutator subgroup of R. The latter have been an object of investigation for more than forty years, due to their intriguing feature of having non-trivial torsion under certain conditions. This was first discovered for the case where R = F0. For arbitrary F and R, if there is torsion in F=[R0; F], it is bound to be contained i
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Mathews, Chad Ullery William D. "Mixed groups with decomposition bases and global k-groups." Auburn, Ala., 2006. http://repo.lib.auburn.edu/2006%20Summer/Theses/MATHEWS_CHAD_59.pdf.

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Nuez, 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.

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MACEDO, Silvio Sandro Alves de. "Comutatividade fraca por bijeção entre grupos abelianos." Universidade Federal de Goiás, 2010. http://repositorio.bc.ufg.br/tede/handle/tde/1973.

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Made available in DSpace on 2014-07-29T16:02:23Z (GMT). No. of bitstreams: 1 silvio sandro.pdf: 761623 bytes, checksum: 55f280c9ca185766a1ed91423c5edfad (MD5) Previous issue date: 2010-06-28<br>The group of weak commutativity for bijection G(H;K;&#963;) = {H;K|[h;h&#963;] = 1, for all h H} belongs is defined as the quotient of the free product H * K the normal closure of {[h;h&#963;] : h belongs to all H} in H * K. In this dissertation, we studied the results obtained in 2009 by Sidka and Oliveira [7] that support the following conjecture: If H,K ~= Zp X...X Zp, then G(H,K,&#963;)is a p-grou
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楊蕙芝. "Finite rank torsion free abelian group." Thesis, 1990. http://ndltd.ncl.edu.tw/handle/68494763600973477471.

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Chen, Yung-Chain, and 陳永清. "On Hom Of Finite Rank Torsion Free Abelian Group." Thesis, 1993. http://ndltd.ncl.edu.tw/handle/87646784711705670555.

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碩士<br>淡江大學<br>數學系<br>81<br>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 res
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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.

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碩士<br>淡江大學<br>數學系<br>81<br>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
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Books on the topic "Free abelian group"

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Ilya, Kazachkov, ed. On systems of equations over free partially commutative groups. American Mathematical Society, 2011.

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Eklof, Paul C. Almost free modules: Set-theoretic methods. North-Holland, 1990.

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H, Mekler Alan, ed. Almost free modules: Set-theoretic models. North Holland, 2002.

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Eklof, P. C., and A.H. Mekler†. Almost Free Modules: Set-theoretic Methods (North-Holland Mathematical Library). North Holland, 2002.

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Direct Sum Decompositions of Torsion-Free Finite Rank Groups (Pure and Applied Mathematics). Chapman & Hall/CRC, 2007.

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Book chapters on the topic "Free abelian group"

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Călugăreanu, Grigore, Simion Breaz, Ciprian Modoi, Cosmin Pelea, and Dumitru Vălcan. "Torsion-free groups." In Exercises in Abelian Group Theory. Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-017-0339-0_18.

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Călugăreanu, Grigore, Simion Breaz, Ciprian Modoi, Cosmin Pelea, and Dumitru Vălcan. "Torsion-free groups." In Exercises in Abelian Group Theory. Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-017-0339-0_8.

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Arnold, David M. "Torsion-Free Abelian Groups." In Abelian Groups and Representations of Finite Partially Ordered Sets. Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4419-8750-1_2.

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Blass, Andreas, John Irwin, and Greg Schlitt. "Some Abelian Groups with Free Duals." In Abelian Groups and Modules. Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-011-0443-2_6.

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Mader, Adolf. "Almost Completely Decomposable Torsion-Free Abelian Groups." In Abelian Groups and Modules. Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-011-0443-2_28.

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Hjorth, Greg. "Around nonclassifiability for countable torsion free abelian groups." In Abelian Groups and Modules. Birkhäuser Basel, 1999. http://dx.doi.org/10.1007/978-3-0348-7591-2_22.

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Arnold, D., and M. Dugas. "Locally Free Finite Rank Butler Groups and Near Isomorphism." In Abelian Groups and Modules. Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-011-0443-2_4.

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Fomin, Alexander A., and William J. Wickless. "Categories of Mixed and Torsion-Free Finite Rank Abelian Groups." In Abelian Groups and Modules. Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-011-0443-2_14.

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Blass, Andreas, and John Irwin. "Basic subgroups and a freeness criterion for torsion-free abelian groups." In Abelian Groups and Modules. Birkhäuser Basel, 1999. http://dx.doi.org/10.1007/978-3-0348-7591-2_20.

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Melnikov, Alexander G. "Enumerations and Torsion Free Abelian Groups." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-73001-9_59.

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Conference papers on the topic "Free abelian group"

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Blagoveshchenskaya, E. A., V. V. Garbaruk, I. V. Kuznetsova, et al. "Common Features of Algorithmic Approaches to Sub-word Parallelism and Torsion-free Abelian Group Decompositions." In 2019 IEEE International Conference on Electrical Engineering and Photonics (EExPolytech). IEEE, 2019. http://dx.doi.org/10.1109/eexpolytech.2019.8906863.

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Pelissetto, Andrea, Sergio Caracciolo, and Andrea Montanari. "Discrete non-Abelian groups and asymptotically free models." In International Europhysics Conference on High Energy Physics. Sissa Medialab, 2001. http://dx.doi.org/10.22323/1.007.0230.

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