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- W2081368125 abstract "Let G be a finite solvable group, and let F ( G ) be its Fitting subgroup. We prove that there is a universal bound for the derived length of G / F ( G ) in terms of the number of distinct conjugacy class sizes of G . This result is asymptotically best possible. It is based on the following result on orbit sizes in finite linear group actions: If G is a finite solvable group and V a finite faithful irreducible G -module of characteristic r , then there is a universal logarithmic bound for the derived length of G in terms of the number of distinct r ′ -parts of the orbit sizes of G on V . This is a refinement of the author's previous work on orbit sizes." @default.
- W2081368125 created "2016-06-24" @default.
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- W2081368125 date "2006-01-01" @default.
- W2081368125 modified "2023-09-28" @default.
- W2081368125 title "Derived length and conjugacy class sizes" @default.
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- W2081368125 doi "https://doi.org/10.1016/j.aim.2004.11.002" @default.
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