Toward a Sharp Baer–Suzuki Theorem for the π-Radical: Exceptional Groups of Small Rank.

Let π be a proper subset of the set of all prime numbers. Denote by r the least prime number not in π, and put m = r, if r = 2, 3, and m = r − 1 if r ≥ 5. We look at the conjecture that a conjugacy class D in a finite group G generates a π-subgroup in G (or, equivalently, is contained in the π-radical) iff any m elements from D generate a π-group. Previously, this conjecture was confirmed for finite groups whose every non-Abelian composition factor is isomorphic to a sporadic, alternating, linear or unitary simple group. Now it is confirmed for groups the list of composition factors of which is added up by exceptional groups of Lie type 2B2(q), 2G2(q), G2(q), and 3D4(q). [ABSTRACT FROM AUTHOR]