Finite groups with exactly three \(p\)-regular classes (Q1193245)
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scientific article; zbMATH DE number 62223
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Finite groups with exactly three \(p\)-regular classes |
scientific article; zbMATH DE number 62223 |
Statements
Finite groups with exactly three \(p\)-regular classes (English)
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27 September 1992
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The following Theorem is proved: Let \(G\) be a finite nonsolvable group with \(O_ p(G)=1\). If \(G\) has exactly three \(p'\)-conjugacy classes, then either \(p=2\) and \(G \cong \Sigma_ 5\), \(PGL_ 2(7)\), \(M_{10}\), \(P \Gamma L_ 2(9)\) or \(p=3\) and \(G \cong P \Gamma L_ 2(8)\) or \(p=5\) and \(G \cong A_ 5\). The proof depends on the classification of finite simple groups.
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\(p\)-regular classes
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number of irreducible Brauer characters
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finite nonsolvable group
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classification of finite simple groups
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