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• W2951247330 abstract "We prove that there exists a constant $k$ with the property: if is a conjugacy class of a finite group $G$ such that every $k$ elements of $calC$ generate a solvable subgroup then generates a solvable subgroup. In particular, using the Classification of Finite Simple Groups, we show that we can take $k=4$. We also present proofs that do not use the Classification theorem. The most direct proof gives a value of $k=10$. By lengthening one of our arguments slightly, we obtain a value of $k=7$." @default.
• W2951247330 created "2019-06-27" @default.
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• W2951247330 date "2009-02-10" @default.
• W2951247330 modified "2023-09-27" @default.
• W2951247330 title "Characterizations of the Solvable Radical" @default.
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