子群的核平凡或正规闭包极大的有限p群

Finite p-Groups with a Trivial Core or the Normal Closure Index p for Every Non-normal Abelian Subgroup

称有限p群G为ACT群,如果对每个交换子群H,其正规核H_(G)=1或H_(G)=H.又称p群G是CC群,如果对每个非正规交换子群H,有H_(G)=1或H^(G)在G中的指数为p.本文分类了ACT群和CC群.

A finite p-group G is called an ACT-group if the core H_(G)=1 or H_(G)=H for every abelian subgroup H.And a p-group G is called a CC-group if H_(G)=1 or H_(G)=H^(G) has index p for every non-normal abelian subgroup H.In this paper,the authors classify the ACT-groups and the CC-groups.