Good action on a finite group

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Ercan G. , Güloğlu İ. Ş. , Jabara E.

JOURNAL OF ALGEBRA, cilt.560, ss.486-501, 2020 (SCI İndekslerine Giren Dergi) identifier identifier


Let G and A be finite groups with A acting on G by automorphisms. In this paper we introduce the concept of "good action"; namely we say the action of A on G is good, if H = [H, B]C-H (B) for every subgroup B of A and every B-invariant subgroup H of G. This definition allows us to prove a new noncoprime Hall-Higman type theorem.