Antisymmetric mappings for finite solvable groups (Q1383596)
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scientific article; zbMATH DE number 1145410
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Antisymmetric mappings for finite solvable groups |
scientific article; zbMATH DE number 1145410 |
Statements
Antisymmetric mappings for finite solvable groups (English)
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9 July 1998
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The author shows that every non-Abelian solvable group \(G\) possesses an antisymmetric mapping, that is a bijection \(\varphi\colon G\to G\) for which holds \(g\varphi(h)\neq h\varphi(g)\) for all \(g,h\in G\) with \(g\neq h\). The proof is constructive and runs via the investigation of a minimal counterexample.
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complete mappings
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modular \(p\)-groups
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solvable groups
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antisymmetric mappings
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