Abstract
Let G be a finite group and suppose that P is a soluble {2, 3}′-subgroup of G. The reader will lose only a little by assuming that P is a subgroup of prime order p > 3. ∑G(P)={A⩽G|A is soluble and A=〈P,Pa〉 for some a ∈ A This set is partially ordered by inclusion and we let ∑ G * ( P ) denote the set of maximal members of ∑G(P).
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