Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Characterizations of the solvable radical

Author(s): Paul Flavell; Simon Guest; Robert Guralnick
Journal: Proc. Amer. Math. Soc. 138 (2010), 1161-1170.
MSC (2010): Primary 20F14, 20D10
Posted: December 2, 2009
MathSciNet review: 2578510
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Abstract: We prove that there exists a constant with the property: if $\mathcal{C}$ is a conjugacy class of a finite group such that every elements of $\mathcal{C}$ generate a solvable subgroup, then $\mathcal{C}$ generates a solvable subgroup. In particular, using the Classification of Finite Simple Groups, we show that we can take . We also present proofs that do not use the Classification Theorem. The most direct proof gives a value of . By lengthening one of our arguments slightly, we obtain a value of .

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