Results 241 to 250 of about 277,944 (294)
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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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Asymptotic Metric Behavior of Random Cayley Graphs of Finite Abelian Groups
Comb., 2016Using methods of Marklof and Strömbergsson we establish several limit laws for metric parameters of random Cayley graphs of finite abelian groups with respect to a randomly chosen set of generators of a fixed size. Doing so we settle a conjecture of Amir
Uri Shapira, Reut Zuck
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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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Abelian Groups with Finitely Approximated Acts
Journal of Mathematical Sciences, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kozhukhov, I. B., Tsarev, A. V.
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SYMPLECTIC GEOMETRIES OVER FINITE ABELIAN GROUPS
Mathematics of the USSR-Sbornik, 1971In the paper one investigates symplectic abelian groups that are the group-theoretical analog of symplectic linear spaces. Bibliography: 3 items.
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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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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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Finitely Generated Abelian Groups
1988A group is finitely generated if it has a finite set of generators. Finitely generated abelian groups may be classified. By this we mean we can draw up a list (albeit infinite) of “standard” examples, no two of which are isomorphic, so that if we are presented with an arbitrary finitely generated abelian group, it is isomorphic to one on our list.
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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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