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On the profinite rigidity of free and surface groups. [PDF]
Math AnnMorales I.
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A general recipe to observe non-Abelian gauge field in metamaterials. [PDF]
NanophotonicsLiu B, Xu T, Hang ZH.
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Geometric and arithmetic characterization of [Formula: see text]-module flatness with applications to tensor products. [PDF]
PLoS OneTang JG, Lei HR, Liu M, Peng JY.
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Exact projected entangled pair ground states with topological Euler invariant. [PDF]
Nat CommunWahl TB +4 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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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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