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Homogeneous isosceles-free spaces. [PDF]
Rev R Acad Cienc Exactas Fis Nat A MatBargetz C +3 more
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AUTOMORPHISMS OF FINITE ABELIAN GROUPS
Mathematical Proceedings of the Royal Irish Academy, 2010Summary: We first use elementary methods to analyse the structure of \(\Aut\,G\) where \(G\) is a finite Abelian \(p\)-group with two distinct cyclic factors. This leads us in a natural way to a simple presentation for \(\Aut\,G\). We then generalise these results to the case where \(G\) is an Abelian \(p\)-group with no repeated direct factors.
Bidwell, J. N. S., Curran, M. J.
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On the factorisation of finite abelian groups. II
Acta Mathematica Hungarica, 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.
A D Sands, Sands A D
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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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FORCING A FINITE GROUP TO BE ABELIAN
Mathematical Proceedings of the Royal Irish Academy, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Deaconescu, M. +2 more
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Israel Journal of Mathematics, 1981
Let \(G\) be a finite Abelian group with \(\#G=p\). For \(A,B\subset G\) let \(m(x,A,B)=\#\{(a,b): a+b=x,\;a\in A,\;b\in B\}\). For \(E\subset G\) let \(E'\) denote its complement. The authors prove the following results: \[ \begin{multlined}\sum_{c\in G} |m(x,E,E)+m(x,E',E')-m(x,E,E')-m(x,E',E)|^2= \\ \sum_{c\in G} |m(x,E,-E)+m(x,E',-E')-m(x,E,-E')-m ...
Erdős, Paul, Smith, B.
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Let \(G\) be a finite Abelian group with \(\#G=p\). For \(A,B\subset G\) let \(m(x,A,B)=\#\{(a,b): a+b=x,\;a\in A,\;b\in B\}\). For \(E\subset G\) let \(E'\) denote its complement. The authors prove the following results: \[ \begin{multlined}\sum_{c\in G} |m(x,E,E)+m(x,E',E')-m(x,E,E')-m(x,E',E)|^2= \\ \sum_{c\in G} |m(x,E,-E)+m(x,E',-E')-m(x,E,-E')-m ...
Erdős, Paul, Smith, B.
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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 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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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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A Reciprocity on Finite Abelian Groups Involving Zero-Sum Sequences
SIAM Journal on Discrete Mathematics, 2021Hanbin Zhang
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