A new criterion for p-nilpotency and solvability of finite groups by coprime actions

Abstract Let G and A be finite groups of relative coprime orders and A acts on G via automorphisms. In this paper, we investigate the p-nilpotency and solvability of finite groups in which every maximal A-invariant subgroup of a Sylow p-subgroup of G for some prime p is S-semipermutable. MSC(2000): 20D10, 20D20