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arXiv · 0902.1738

A solvable version of the Baer--Suzuki Theorem

Simon Guest
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Abstract

Suppose that G is a finite group and x in G has prime order p > 3. Then x is contained in the solvable radical of G if (and only if) is solvable for all g in G. If G is an almost simple group and x in G has prime order p > 3 then this implies that there exists g in G such that is not solvable. In fact, this is also true when p=3 with very few exceptions, which are described explicitly.

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Simon Guest. 2009-02-10. A solvable version of the Baer--Suzuki Theorem. https://arxiv.org/abs/0902.1738

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