Lower bounds for the number of conjugacy classes in finite solvable groups
Copyright policy )Lower bounds for the number of conjugacy classes in finite solvable groups
If \(G\) is a finite solvable group of derived length \(d\) (at least 2), and \(k(G)\) denotes the number of conjugacy classes in \(G\), then \(k(G) > | G|^{1/(2^ d-1)}\). Additional lower bounds for \(k(G)\) are derived under additional assumptions, e.g. that \(G\) has a nilpotent maximal subgroup.
- University of Hawaiʻi Sea Grant United States
- University of Hawaii at Manoa United States
- University of Hawaii System United States
derived length, Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks, number of conjugacy classes, nilpotent maximal subgroup, finite solvable group, Arithmetic and combinatorial problems involving abstract finite groups
derived length, Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks, number of conjugacy classes, nilpotent maximal subgroup, finite solvable group, Arithmetic and combinatorial problems involving abstract finite groups
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