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Decomposing Finite Abelian Groups [PDF]
Quantum Information and Computation, 2001 This paper describes a quantum algorithm for efficiently decomposing finite Abelian groups into a product of cyclic groups. Such a decomposition is needed in order to apply the Abelian hidden subgroup algorithm. Such a decomposition (assuming the Generalized Riemann Hypothesis) also leads to an efficient algorithm for computing class numbers (known to ...
Kevin K. H. Cheung, Michele Mosca
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Computational methods for difference families in finite abelian groups
Special Matrices, 2019 Our main objective is to show that the computational methods, developed previously to search for difference families in cyclic groups, can be fully extended to the more general case of arbitrary finite abelian groups.
Ðoković Dragomir Ž. +1 more
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Lattices of finite abelian groups [PDF]
Discrete & Computational Geometry, 2019 We study certain lattices constructed from finite abelian groups. We show that such a lattice is eutactic, thereby confirming a conjecture by B\"ottcher, Eisenbarth, Fukshansky, Garcia, Maharaj. Our methods also yield simpler proofs of two known results:
Ladisch, Frieder
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Simple Finite Non-Abelian Flavor Groups [PDF]
Journal of Mathematical Physics, 2007 The recently measured unexpected neutrino mixing patterns have caused a resurgence of interest in the study of finite flavor groups with two- and three-dimensional irreducible representations.
Christoph Luhn +4 more
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Automorphisms of Finite Abelian Groups [PDF]
The American Mathematical Monthly, 2007 We give an accessible and modern description of the automorphisms of a finite abelian group $G$. Included is an explicit formula for the cardinality of $Aut(G)$.
Hillar, Christopher J., Rhea, Darren
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On Schurity of Finite Abelian Groups [PDF]
Communications in Algebra, 2015 20 ...
Evdokimov, Sergei +2 more
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Internal quantum reference frames for finite Abelian groups [PDF]
Journal of Mathematics and Physics, 2021 Employing internal quantum systems as reference frames is a crucial concept in quantum gravity, gauge theories, and quantum foundations whenever external relata are unavailable.
Philipp A. Hoehn +2 more
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Endomorphism kernel property for finite groups [PDF]
Mathematica Bohemica, 2022 A group $G$ has the endomorphism kernel property (EKP) if every congruence relation $\theta$ on $G$ is the kernel of an endomorphism on $G$. In this note we show that all finite abelian groups have EKP and we show infinite series of finite non-abelian ...
Heghine Ghumashyan, Jaroslav Guričan
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Co-prime order graphs of finite Abelian groups and dihedral groups [PDF]
, 2020 The \textbf{Co-Prime Order Graph} $\Theta (G)$ of a given finite group is a simple undirected graph whose vertex set is the group $G$ itself, and any two vertexes x,y in $\Theta (G)$ are adjacent if and only if $gcd(o(x),o(y))=1$ or prime. In this paper,
Amit Sehgal, Manjeet, Dalip Singh
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On Modified Erdős-Ginzburg-Ziv constants of finite abelian groups
AIMS Mathematics, 2023 Let $ G $ be a finite abelian group with exponent $ \exp(G) $ and $ S $ be a sequence with elements of $ G $. We say $ S $ is a zero-sum sequence if the sum of the elements in $ S $ is the zero element of $ G $.
Yuting Hu, Jiangtao Peng , Mingrui Wang
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