Some Results on partially Hall s-semiembedded subgroups and p-nilpotency of finite groups

Abstract

Let 〖 T〗_1 be subgroup of G. Then 〖 T〗_1 is known as partially Hall s-semiembedded within G (P_HSseG) if There exits T_2⊴G such that T_1 T_2 is s-semi permutable in G (s_sperG ) and〖 T〗_1∩T_2≤(T_1 )_SG, where (T_1 )_SG is created by those subgroups of〖 T〗_1 which are〖 H〗_SseG. In this paper, we investigate notion of partially Hall s-semiembedded subgroups on the structure of a finite group G. Moreover, some new criteria were established for p-nilpotency and supersolvability of a finite group. Our results about formations are extension of some earlier ones theorems available in literature.