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

2009/02/11 by Gordeev, Nikolai, Grunewald, Fritz, Kunyavskii, Boris +1 · 1 citation
#20D06 #20D08 #20D10 #20D25 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.0902.1912

Abstract

We 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∈ 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.

Cited by

• On generation by triality automorphisms

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