ON c-NORMAL AND S-QUASINORMALLY EMBEDDED SUBGROUPS OF A FINITE GROUP

Abstract

If P is a p-group for some prime p we shall write \(\mathcal{M}\)(P) to denote the set of all maximal subgroups of P and \(\mathcal{M}_d\)(P) = {P₁,...,P_d} to denote any set of maximal subgroups of P such that \(\cap_{i=1}^{d}\) P_i = Φ(P) and d is as small as possible.  In this paper, the structure of a finite group G under some assumptions on the c-normal or S-quasinormally embedded subgroups in \(\mathcal{M}_d\)(P), for each prime p, and Sylow p-subgroups P of G is researched.  Some known results are generalized.