An elementary proof that finite groups lack unique product structures (Q1911644)
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scientific article; zbMATH DE number 869809
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An elementary proof that finite groups lack unique product structures |
scientific article; zbMATH DE number 869809 |
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An elementary proof that finite groups lack unique product structures (English)
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3 June 1996
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A slick combinatorial argument is given to prove that if \(G\) is a nontrivial finite group and if \(m\geq 2\) is a fixed integer, then there is no subset \(S\) of \(G\) such that the map \(\Phi:S^m\to G\), defined by \(\Phi(a_1,a_2,\dots,a_m)=a_1a_2\dots a_m\) is a bijection. This result was previously obtained by \textit{D. Dimovski} [J. Algebra 146, No. , 205-209 (1992; Zbl 0752.20038)] using character theory.
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finite groups
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unique product structures
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0.8287844657897949
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0.8281202912330627
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