Baer-Suzuki theorem for the solvable radical of a finite group

摘要

We prove that an element g of prime order q > 3 belongs to the solvable radical R(G) of a finite group if and only if for every x is an element of G the subgroup generated by g and xgx(-1) is solvable. This theorem implies that a finite group G is solvable if and only if ill each conjugacy class of G every two elements generate a solvable subgroup. To cite this article: N. Gordeev et al., C R. Acad. Sci. Paris, Ser. I 347 (2009).