On finite subsets of nonabelian groups with small doubling. (Q2845723)
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scientific article; zbMATH DE number 6203901
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On finite subsets of nonabelian groups with small doubling. |
scientific article; zbMATH DE number 6203901 |
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3 September 2013
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nonabelian groups
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finite subsets
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small doubling
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combinatorial conditions on subsets
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On finite subsets of nonabelian groups with small doubling. (English)
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Let \(A\) be a finite subset of a non-Abelian group \(G\), and \(A^2=\{ab:a,b\in A\}\). It is shown that if \(|A^2|<1.5|A|\), then the set \(H=AA^{-1}=AA^{-1}\) is a subgroup of \(G\), and \(A^2\) is a coset of \(H\), possibly coinciding with \(H\). An earlier version of this result with a sketch of its proof was published by the author [in Teoretiko-Chisl. Issled. Spektru Markov. Struktur. Teor. Slozhen. Mnozhestv, 175-183 (1973; Zbl 0321.10049)] in Russian.
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