A note on Flavell's theorem associated with Frobenius groups

Abstract

Let G be a Frobenius group with the Frobenius kernel K. Suppose that G contains a nontrival subgroup D ⊂eq K such that the normalizer NG(D) ⊂eq K. When D is no 2-group, Flavell proved, without using character theory, that K is a subgroup of G. Based on this result, we further prove that K is a subgroup when D is a 2-group.

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