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Thompson-like characterization of the solvable radical

R. Guralnick·B. Kunyavskii·E. Plotkin·A. Shalev
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Abstract

We prove that the solvable radical of a finite group G coincides with the set of elements y having the following property: for any x in G the subgroup of G generated by x and y is solvable. We present analogues of this result for finite dimensional Lie algebras and some classes of infinite groups. We also consider a similar problem for pairs of elements.

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R. Guralnick, B. Kunyavskii, E. Plotkin, A. Shalev. 2005-08-28. Thompson-like characterization of the solvable radical. https://arxiv.org/abs/math/0504176

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