c-Normality and coprime action in finite groups

Abstract

A subgroup H of a finite group G is called c-normal if there exists a normal subgroup N in G such that G = HN and \(H\cap N \leq core_G (H)\), the largest normal subgroup of G contained in H. c-Normality is a weaker form of normality, introduced by Y.M. Wang, that has led to interesting results and structural criteria of finite groups. In this paper we study c-normality in the coprime action setting so as to obtain several solvability and p-nilpotency criteria in terms of certain subsets of maximal invariant subgroups of a group or of its Sylow subgroups.