From Thompson to Baer-Suzuki: a sharp characterization of the solvable radical

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dc.creatorGordeev, Nikolai
dc.creatorGrunewald, Fritz
dc.creatorKunyavskii, Boris
dc.creatorPlotkin, Eugene
dc.date2009-02-11
dc.date2009-03-27
dc.date.accessioned2026-07-07T12:56:54Z
dc.date.available2026-07-07T12:56:54Z
dc.descriptionWe prove that an element $g$ of prime order $>3$ belongs to the solvable radical $R(G)$ of a finite (or, more generally, a linear) group if and only if for every $x\in G$ the subgroup generated by $g, xgx^{-1}$ is solvable. This theorem implies that a finite (or a linear) group $G$ is solvable if and only if in each conjugacy class of $G$ every two elements generate a solvable subgroup.
dc.description28 pages
dc.identifierhttps://arxiv.org/abs/0902.1912
dc.identifierhttp://arxiv.org/abs/0902.1912
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/224745
dc.subjectGroup Theory
dc.subject20D10; 20D25; 20D06; 20D08
dc.titleFrom Thompson to Baer-Suzuki: a sharp characterization of the solvable radical
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