On nearly Hall S-Semi Embedded Subgroups and P-Nilpotency of Finite Groups

A subgroup〖 S〗_1≤G, is said to be nearly Hall s-semiembedded within G (N_HSseG) if there exits S_2⊴G such that S_1 S_2 is S-semiembedded in G( s_seG) and〖 S〗_1∩S_2≤(S_1 )_nSG, where (S_1 )_nSG is created by those subgroups of 〖 S〗_1 which are Hall S-semiembedded in G 〖( H〗_SseG). In this paper, we investigate new notion of nearly Hall s-semiembedded subgroups on the structure of a finite group. Moreover, some new criteria were established for p-nilpotency and supersolvability of a finite group using nearly Hall s-semiembedded subgroups. Our results about formations are extension of some earlier theorems available in literature.