Relevant bibliographies by topics / Finite abelian group

Contents

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

Academic literature on the topic 'Finite abelian group'

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

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Journal articles on the topic "Finite abelian group"

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JAIN, VIVEK K., PRADEEP K. RAI, and MANOJ K. YADAV. "ON FINITE p-GROUPS WITH ABELIAN AUTOMORPHISM GROUP." International Journal of Algebra and Computation 23, no. 05 (August 2013): 1063–77. http://dx.doi.org/10.1142/s0218196713500161.

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We construct, for the first time, various types of specific non-special finite p-groups having abelian automorphism group. More specifically, we construct groups G with abelian automorphism group such that γ2(G) < Z(G) < Φ(G), where γ2(G), Z(G) and Φ(G) denote the commutator subgroup, the center and the Frattini subgroup of G respectively. For a finite p-group G with elementary abelian automorphism group, we show that at least one of the following two conditions holds true: (i) Z(G) = Φ(G) is elementary abelian; (ii) γ2(G) = Φ(G) is elementary abelian, where p is an odd prime. We construct examples to show the existence of groups G with elementary abelian automorphism group for which exactly one of the above two conditions holds true.
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Pranjali, Mukti Acharya, and Purnima Gupta. "Finite Abelian Group Labeling." Electronic Notes in Discrete Mathematics 48 (July 2015): 255–58. http://dx.doi.org/10.1016/j.endm.2015.05.038.

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Carocca, Angel, Herbert Lange, and Rubí E. Rodríguez. "Abelian varieties with finite abelian group action." Archiv der Mathematik 112, no. 6 (April 20, 2019): 615–22. http://dx.doi.org/10.1007/s00013-018-1291-9.

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K. Thomas, Eldho, Nadya Markin, and Frédérique Oggier. "On Abelian group representability of finite groups." Advances in Mathematics of Communications 8, no. 2 (2014): 139–52. http://dx.doi.org/10.3934/amc.2014.8.139.

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A. Zain, Adnan. "On Group Codes Over Elementary Abelian Groups." Sultan Qaboos University Journal for Science [SQUJS] 8, no. 2 (June 1, 2003): 145. http://dx.doi.org/10.24200/squjs.vol8iss2pp145-151.

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For group codes over elementary Abelian groups we present definitions of the generator and the parity check matrices, which are matrices over the ring of endomorphism of the group. We also lift the theorem that relates the parity check and the generator matrices of linear codes over finite fields to group codes over elementary Abelian groups. Some new codes that are MDS, self-dual, and cyclic over the Abelian group with four elements are given.
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Carocca, Angel, Herbert Lange, and Rubí E. Rodríguez. "RETRACTED ARTICLE: Abelian varieties with finite abelian group action." Archiv der Mathematik 112, no. 4 (October 8, 2018): 447–48. http://dx.doi.org/10.1007/s00013-018-1244-3.

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Li, Xiaolong, Siren Cai, Weiming Zhang, and Bin Yang. "Matrix embedding in finite abelian group." Signal Processing 113 (August 2015): 250–58. http://dx.doi.org/10.1016/j.sigpro.2015.02.007.

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Gao, Yubin, and Guoping Tang. "K2 of finite abelian group algebras." Journal of Pure and Applied Algebra 213, no. 7 (July 2009): 1201–7. http://dx.doi.org/10.1016/j.jpaa.2008.09.015.

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PILLADO, CRISTINA GARCÍA, SANTOS GONZÁLEZ, CONSUELO MARTÍNEZ, VICTOR MARKOV, and ALEXANDER NECHAEV. "GROUP CODES OVER NON-ABELIAN GROUPS." Journal of Algebra and Its Applications 12, no. 07 (May 16, 2013): 1350037. http://dx.doi.org/10.1142/s0219498813500370.

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Let G be a finite group and F a field. We show that all G-codes over F are abelian if the order of G is less than 24, but for F = ℤ5 and G = S4 there exist non-abelian G-codes over F, answering to an open problem posed in [J. J. Bernal, Á. del Río and J. J. Simón, An intrinsical description of group codes, Des. Codes Cryptogr.51(3) (2009) 289–300]. This problem is related to the decomposability of a group as the product of two abelian subgroups. We consider this problem in the case of p-groups, finding the minimal order for which all p-groups of such order are decomposable. Finally, we study if the fact that all G-codes are abelian remains true when the base field is changed.
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Han, Dongchun, Yuan Ren, and Hanbin Zhang. "On ∗-clean group rings over abelian groups." Journal of Algebra and Its Applications 16, no. 08 (August 9, 2016): 1750152. http://dx.doi.org/10.1142/s0219498817501523.

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An associative ring with unity is called clean if each of its elements is the sum of an idempotent and a unit. A clean ring with involution ∗ is called ∗-clean if each of its elements is the sum of a unit and a projection (∗-invariant idempotent). In a recent paper, Huang, Li and Yuan provided a complete characterization that when a group ring [Formula: see text] is ∗-clean, where [Formula: see text] is a finite field and [Formula: see text] is a cyclic group of an odd prime power order [Formula: see text]. They also provided a necessary condition and a few sufficient conditions for [Formula: see text] to be ∗-clean, where [Formula: see text] is a cyclic group of order [Formula: see text]. In this paper, we extend the above result of Huang, Li and Yuan from [Formula: see text] to [Formula: see text] and provide a characterization of ∗-clean group rings [Formula: see text], where [Formula: see text] is a finite abelian group and [Formula: see text] is a field with characteristic not dividing the exponent of [Formula: see text].
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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.

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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.

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Giangreco, Maidana Alejandro José. "Cyclic abelian varieties over finite fields." Thesis, Aix-Marseille, 2019. http://www.theses.fr/2019AIXM0316.

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L'ensemble A(k) des points rationnels d'une variété abélienne A définie sur un corps fini k forme un groupe abélien fini. Ce groupe convient pour des multiples applications, et sa structure est très importante. Connaître les possibles structures de groupe des A(k) et quelques statistiques est donc fondamental. Dans cette thèse, on s'intéresse aux "variétés cycliques", i.e. variétés abéliennes définies sur des corps finis avec groupe des points rationnels cyclique.Les isogénies nous donnent une classification plus grossière que celle donnée par les classes d'isomorphisme des variétés abéliennes, mais elles offrent un outil très puissant en géométrie algébrique. Chaque classe d'isogénie est déterminée par son polynôme de Weil. On donne un critère pour caractériser les "classes d'isogénies cycliques", i.e. classes d'isogénies de variétés abéliennes définies sur des corps finis qui contiennent seulement des variétés cycliques. Ce critère est basé sur le polynôme de Weil de la classe d'isogénie.À partir de cela, on donne des bornes de la proportion de classes d'isogénies cycliques parmi certaines familles de classes d'isogénies paramétrées par ses polynômes de Weil.On donne aussi la proportion de classes d'isogénies cycliques "locaux" parmi les classes d'isogénie définies sur des corps finis mathbb{F}_q avec q éléments, quand q tend à l'infini
The 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
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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.

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Thesis (M.A.) -- University of Maryland, College Park, 2005.
Thesis 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.
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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.

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Deligne and Howe described polarized abelian varieties over finite fields in terms of finitely generated free Z-modules satisfying a list of easy to state axioms. In this thesis we address the problem of developing an effective algorithm to compute isomorphism classes of (principally) polarized abelian varieties over a finite field, together with their automorphism groups. Performing such computations requires the knowledge of the ideal classes (both invertible and non-invertible) of certain orders in number fields. Hence we describe a method to compute the ideal class monoid of an order and we produce concrete computations in dimension 2, 3 and 4.
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Ngcibi, 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.

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We determine the number and nature of distinct equivalence classes of fuzzy subgroups of finite Abelian p-group G of rank two under a natural equivalence relation on fuzzy subgroups. Our discussions embrace the necessary theory from groups with special emphasis on finite p-groups as a step towards the classification of crisp subgroups as well as maximal chains of subgroups. Unique naming of subgroup generators as discussed in this work facilitates counting of subgroups and chains of subgroups from subgroup lattices of the groups. We cover aspects of fuzzy theory including fuzzy (homo-) isomorphism together with operations on fuzzy subgroups. The equivalence characterization as discussed here is finer than isomorphism. We introduce the theory of keychains with a view towards the enumeration of maximal chains as well as fuzzy subgroups under the equivalence relation mentioned above. We discuss a strategy to develop subgroup lattices of the groups used in the discussion, and give examples for specific cases of prime p and positive integers n,m. We derive formulas for both the number of maximal chains as well as the number of distinct equivalence classes of fuzzy subgroups. The results are in the form of polynomials in p (known in the literature as Hall polynomials) with combinatorial coefficients. Finally we give a brief investigation of the results from a graph-theoretic point of view. We view the subgroup lattices of these groups as simple, connected, symmetric graphs.
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Mariani, 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/.

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Nuovi sviluppi nel campo nelle tecniche sperimentali potrebbero presto permettere la realizzazione di simulatori quantistici, ovvero di sistemi quantomeccanici realizzabili sperimentalmente che descrivano una specifica Hamiltoniana di nostra scelta. Una volta costruito il sistema, si possono effettuare esperimenti per studiare il comportamento della teoria descritta dall'Hamiltoniana scelta. Un'interessante applicazione riguarda le teorie di gauge non-Abeliane come la Cromodinamica Quantistica, per le quali si hanno un certo numero di problemi irrisolti, in particolare nella regione a potenziale chimico finito. La principale sfida teorica per la realizzazione di un simulatore quantistico è quella di rendere lo spazio di Hilbert della teoria di gauge finito-dimensionale. Infatti in un esperimento si possono controllare realisticamente solo alcuni gradi di libertà del sistema quantistico, e certamente solo un numero finito. Seguendo alcune linee già tracciate in letteratura, nel presente lavoro ottieniamo uno spazio di Hilbert finito-dimensionale sostituendo il gruppo di gauge - un gruppo di Lie - con un gruppo finito, ad esempio uno dei suoi sottogruppi. Dopo una rassegna della teoria di Yang-Mills nel continuo e su reticolo, ne diamo la formulazione Hamiltoniana enfatizzando l'introduzione del potenziale chimico. A seguire, introduciamo le teorie basate su un qualsiasi gruppo di gauge finito, e proponiamo una soluzione ad un problema irrisolto di tali teorie, cioè la determinazione degli autovalori della densità di energia elettrica. Effettuiamo inoltre alcuni calcoli analitici della tensione di stringa in teorie con gruppo di gauge finito, e risolveremo esattamente alcune di esse in un caso semplificato. A finire, studieremo il comportamento dello stato fondamentale di tali teorie tramite un metodo variazionale, e offriremo alcune considerazioni conclusive.
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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 condition is true when A is an abelian group whose order is a product of three primes which are coprime to 6 and jGj is odd.
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Decker, Erin. "On the construction of groups with prescribed properties." Diss., Online access via UMI:, 2008.

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Assis, 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.

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Made available in DSpace on 2015-05-15T11:46:11Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 411324 bytes, checksum: 65de8bf46cc2dff58911edbcb15868ca (MD5) Previous issue date: 2011-09-09
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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.
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Books on the topic "Finite abelian group"

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Fourier analysis on finite Abelian groups. Boston: Birkhäuser, 2009.

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Luong, Bao. Fourier Analysis on Finite Abelian Groups. Boston: Birkhäuser Boston, 2009. http://dx.doi.org/10.1007/978-0-8176-4916-6.

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

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Stankovic, Radomir S. Fourier analysis on finite groups with applications in signal processing and system design. Hoboken, NJ: Wiley & Sons Inc., 2005.

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Symmetric functions and Hall polynomials. 2nd ed. Oxford: Clarendon Press, 1995.

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Stanković, Radomir S. Fourier analysis on finite groups with applications in signal processing and system design. Piscataway, NJ: IEEE Press, 2005.

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Stanković, Radomir S. Fourier Analysis on Finite Groups with Applications in Signal Processing and System Design. New York: John Wiley & Sons, Ltd., 2005.

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Jong, Aise Johan de. Moduli of Abelian Varieties and Dieudonné Modules of Finite Group Schemes. 1996.

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M¨uhlherr, Bernhard, Holger P. Petersson, and Richard M. Weiss. Moufang Quadrangles. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691166902.003.0004.

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This chapter proves various results about Moufang quadrangles. It first considers the notions of a proper involutory set, a proper indifferent set, and a proper anisotropic pseudo-quadratic space. It then shows that the root group sequence Ω‎ is isomorphic to a root group sequence of exactly one of six types relating to some proper involutory set, some non-trivial anisotropic quadratic space, some proper indifferent set, some proper anisotropic pseudo-quadratic space, and some quadratic space. It also describes the degree of a finite purely inseparable field extension as a power of the characteristic, an isomorphism from a root group sequence of Δ‎ to the Moufang quadrangle, and abelian and non-abelian groups.
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Luong, Bao. Fourier Analysis on Finite Abelian Groups. Springer, 2010.

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Book chapters on the topic "Finite abelian group"

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Pyber, L. "How Abelian is a Finite Group?" In Algorithms and Combinatorics, 372–84. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-60408-9_27.

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Pyber, Lásló. "How Abelian is a Finite Group?" In The Mathematics of Paul Erdős I, 409–23. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7258-2_25.

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N. Mordeson, John, Kiran R. Bhutani, and Azriel Rosenfeld. "Equivalence of Fuzzy Subgroups of Finite Abelian Groups." In Fuzzy Group Theory, 201–38. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/10936443_8.

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Kitture, Rahul Dattatraya, and Manoj K. Yadav. "Finite Groups with Abelian Automorphism Groups: A Survey." In Group Theory and Computation, 119–40. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-2047-7_7.

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Desmedt, Yvo, and Yair Frankel. "Perfect Zero-Knowledge Sharing Schemes over any Finite Abelian Group." In Sequences II, 369–78. New York, NY: Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4613-9323-8_28.

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Karagiorgos, Gregory, and Dimitrios Poulakis. "An Algorithm for Computing a Basis of a Finite Abelian Group." In Algebraic Informatics, 174–84. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21493-6_11.

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King, Brian. "Randomness Required for Linear Threshold Sharing Schemes Defined over Any Finite Abelian Group." In Information Security and Privacy, 376–91. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/3-540-47719-5_30.

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Desmedt, Yvo, Brian King, Wataru Kishimoto, and Kaoru Kurosawa. "A comment on the efficiency of secret sharing scheme over any finite abelian group." In Information Security and Privacy, 391–402. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/bfb0053750.

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Kurzweil, Hans, and Bernd Stellmacher. "Abelian Groups." In The Theory of Finite Groups, 43–54. New York, NY: Springer New York, 2004. http://dx.doi.org/10.1007/0-387-21768-1_2.

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Tolimieri, Richard, Myoung An, and Chao Lu. "Finite Abelian Groups." In Signal Processing and Digital Filtering, 37–50. New York, NY: Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4612-1948-4_3.

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Conference papers on the topic "Finite abelian group"

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Yang, Qinqin, and Zhongping Qin. "An Algorithm for Computing Characteristic Matrices of Group Codes over Finite Abelian Groups." In 2008 4th International Conference on Wireless Communications, Networking and Mobile Computing (WiCOM). IEEE, 2008. http://dx.doi.org/10.1109/wicom.2008.365.

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Chew, C. Y., A. Y. M. Chin, and C. S. Lim. "The number of subgroups of a finite abelian p-group of rank 4." In THE 22ND NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES (SKSM22): Strengthening Research and Collaboration of Mathematical Sciences in Malaysia. AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4932475.

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Yu, Chia-An, Tak-Shing Chan, and Yi-Hsuan Yang. "Low-Rank Matrix Completion over Finite Abelian Group Algebras for Context-Aware Recommendation." In CIKM '17: ACM Conference on Information and Knowledge Management. New York, NY, USA: ACM, 2017. http://dx.doi.org/10.1145/3132847.3133057.

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Moradipour, Kayvan, and Sheila Ilangovan. "Size of conjugacy classes in a finite non-abelian group of negative type." In PROCEEDINGS OF THE 27TH NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES (SKSM27). AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0018729.

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Chattopadhyay, Arkadev, and Shachar Lovett. "Linear Systems over Finite Abelian Groups." In 2011 IEEE Annual Conference on Computational Complexity (CCC). IEEE, 2011. http://dx.doi.org/10.1109/ccc.2011.25.

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Farzan, Arash, and J. Ian Munro. "Succinct representation of finite abelian groups." In the 2006 international symposium. New York, New York, USA: ACM Press, 2006. http://dx.doi.org/10.1145/1145768.1145788.

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Nwabueze, Kenneth K., Norhayati Hamzah, and Saiful A. Husain. "The Abelian Index of finite groups." In Third Asian Mathematical Conference 2000. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812777461_0038.

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Jia, Xingde. "Extremal Cayley Digraphs of Finite Abelian Groups." In 2011 IEEE 14th International Conference on Computational Science and Engineering (CSE). IEEE, 2011. http://dx.doi.org/10.1109/cse.2011.88.

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KANEMITSU, SHIGERU, and MICHEL WALDSCHMIDT. "MATRICES OF FINITE ABELIAN GROUPS, FINITE FOURIER TRANSFORM AND CODES." In Proceedings of the 6th China–Japan Seminar. WORLD SCIENTIFIC, 2013. http://dx.doi.org/10.1142/9789814452458_0005.

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Fawzi, Hamza, James Saunderson, and Pablo A. Parrilo. "Sparse sum-of-squares certificates on finite abelian groups." In 2015 54th IEEE Conference on Decision and Control (CDC). IEEE, 2015. http://dx.doi.org/10.1109/cdc.2015.7403148.

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