Finite groups with exactly threep-regular classes
Copyright policy )Finite groups with exactly threep-regular classes
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.
- Shinshu University Japan
- Shinshu University Japan
classification of finite simple groups, finite nonsolvable group, Modular representations and characters, number of irreducible Brauer characters, \(p\)-regular classes, Finite simple groups and their classification, Group rings of finite groups and their modules (group-theoretic aspects), Arithmetic and combinatorial problems involving abstract finite groups
classification of finite simple groups, finite nonsolvable group, Modular representations and characters, number of irreducible Brauer characters, \(p\)-regular classes, Finite simple groups and their classification, Group rings of finite groups and their modules (group-theoretic aspects), Arithmetic and combinatorial problems involving abstract finite groups
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