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• W2048813750 abstract "Suppose that $G$ is a finite group and $x in G$ has prime order $p ge 5$. Then $x$ is contained in the solvable radical of $G$, $O_{infty }(G)$, if (and only if) $langle x,x^g rangle$ is solvable for all $g in G$. If $G$ is an almost simple group and $x in G$ has prime order $p ge 5$, then this implies that there exists $g in G$ such that $langle x,x^g rangle$ is not solvable. In fact, this is also true when $p=3$ with very few exceptions, which are described explicitly." @default.
• W2048813750 created "2016-06-24" @default.
• W2048813750 creator A5064594893 @default.
• W2048813750 date "2010-11-01" @default.
• W2048813750 modified "2023-09-27" @default.
• W2048813750 title "A solvable version of the Baer–Suzuki theorem" @default.
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• W2048813750 doi "https://doi.org/10.1090/s0002-9947-2010-04932-3" @default.
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