A conjecture on the number of conjugacy classes in a \(p\)-solvable group (Q1912783)
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scientific article; zbMATH DE number 878289
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A conjecture on the number of conjugacy classes in a \(p\)-solvable group |
scientific article; zbMATH DE number 878289 |
Statements
A conjecture on the number of conjugacy classes in a \(p\)-solvable group (English)
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30 October 1996
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Let \(G\) be a finite group, \(k(G)\) the number of conjugacy classes of \(G\) and \(p\in\pi(G)\) a prime. It is proved that if \(G\) is a solvable group then \(k(G/O_p(G))\leq|G|_{p'}\) and \(k(G/F(G))\) is bounded by the index of a nilpotent injector of \(G\).
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finite groups
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number of conjugacy classes
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solvable groups
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nilpotent injectors
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