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The Reconstructibility of Finite Abelian Groups
Combinatorics, Probability and Computing, 2004Summary: Given a subset \(S\) of an Abelian group \(G\) and an integer \(k\geq 1\), the `\(k\)-deck' of \(S\) is the function that assigns to every \(T\subseteq G\) with at most \(k\) elements the number of elements \(g\in G\) with \(g+T\subseteq S\).
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On Finite Groups with an Abelian Sylow Group
Canadian Journal of Mathematics, 1962We shall consider finite groups of order of g which satisfy the following condition:(*) There exists a prime p dividing g such that if P ≠ 1 is an element of p-Sylow group ofthen the centralizer(P) of P incoincides with the centralizer() of in.This assumption is satisfied for a number of important classes of groups.
Brauer, R., Leonard, H. S. jun.
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On the Factorization of Finite Abelian Groups
Indagationes Mathematicae (Proceedings), 1953This article also appeared in Indagationes mathematicae.
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On the factorisation of finite abelian groups. II
Acta Mathematica Academiae Scientiarum Hungaricae, 1962A famous conjecture of Minkowski, concerning the columnation of space-filling lattices, was first proved by Hajos in 1941 by translating the problem into one involving finite abelian groups. The problem solved by Hajos was one concerning a special type of factorisation of finite abelian groups.
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Bent functions from a finite abelian group into a finite abelian group
Discrete Mathematics and Applications, 2002AbstractWe introduce the notions of an absolutely non-homomorphic function, a minimal function (farthest from homomorphisms) and a bent function, and prove that the class of bent functions coincides with the class of absolutely non-homomorphic functions, a function is uniquely determined by the distances to homomorphisms with shifts, and that in the ...
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Phase Retrievable Projective Representation Frames for Finite Abelian Groups
, 2019Lan Li +4 more
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Complete decompositions of finite abelian groups
Applicable Algebra in Engineering, Communication and Computing, 2018A. Chin, Huey Voon Chen
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2002
In this chapter we present the complete theory developed in this book for the simplest case to which it can be applied, that of a finite abelian group. In this case no analytic tools are required, and only a small amount of group theory is needed in order to understand the concept of the duality and the Plancherel theorem.
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In this chapter we present the complete theory developed in this book for the simplest case to which it can be applied, that of a finite abelian group. In this case no analytic tools are required, and only a small amount of group theory is needed in order to understand the concept of the duality and the Plancherel theorem.
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First-Order Queries on Finite Abelian Groups
Annual Conference for Computer Science Logic, 2015S. Bova, Barnaby Martin
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