Finite groups with some \mathcal{HC}-subgroups

Let G be a finite group. A subgroup H of G is called an \mathcal{H}{-}subgroup in G if H^{g}\cap N_{G}(H)\leq H for all g\in G. A subgroup H of G is called an \mathcal{H}{ C-}subgroup in G if there exists a normal subgroup T of G such that G=HT and H^{g}\cap N_{T}(H)\leq H for all g\in G. In this paper, we give some new criteria for p-nilpotency and supersolvability of a group G when certain subgroups of prime power orders of G are \mathcal{H}{ C-}subgroups.

کلیدواژه ها:

\mathcal{H} C-subgroup ، p-nilpotent group ، Supersolvable group