A Solvable Version of the Baer–suzuki Theorem
نویسنده
چکیده
Suppose that G is a finite group and x ∈ G has prime order p ≥ 5. Then x is contained in the solvable radical of G, O∞(G), if (and only if) 〈x, xg〉 is solvable for all g ∈ G. If G is an almost simple group and x ∈ G has prime order p ≥ 5, then this implies that there exists g ∈ G such that 〈x, xg〉 is not solvable. In fact, this is also true when p = 3 with very few exceptions, which are described explicitly.
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