On products of sets in groups (Q1334936)
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scientific article; zbMATH DE number 644727
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On products of sets in groups |
scientific article; zbMATH DE number 644727 |
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On products of sets in groups (English)
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26 September 1994
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Let \(G\) be a group, \(B\) a finite subset of \(G\) containing 1, and \(A\) a non-empty finite subset of \(G\). The authors prove the following result: Either \(AB= A\langle B\rangle\) or \(| AB|\geq | A|+ \lfloor{2\over 3}(| B|+ 1)\rfloor\) if \(B= B^{-1}\) or \(B\cap B^{-1}=\{1\}\). The proof is based on properties of Cayley graphs.
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automorphism group
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Cayley graphs
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