Inner p-closed Groups and Their Gneralization

Abstract:

      A non-p-closed group G is called quasi-p-closed if G has a proper subgroup H suchthat each of proper subgroup K of G not contained in H isp-closed. In this paper,we-obtain the following theorems:Theorem 1 Let G be a qhasi-p-closed group。 I.If G is solvable, then II. If G is non- solvable, then a)G/φ(G)a non-abelian simple group.b) G=N×1<α>,where N/φ(N) is a non- abelian simple group.Theorem 2 Inner-5-closed G has the following two types: 1.Inner p-nilPotent groups of order 5^αp^β. II G/φ(G)is isomorphic with ＰＳＬ（２，５），or Ｓ_ｚ（5^ｑ）(where q is an odd prime).