On A Class Of Finite Core(m)-groups

For m a positive integer, a group G is called core(m)-group, if\H:Hg\\P1P2…Pm(P1P2,…,Pm is prime) for every subgroup H of G, where HG is the normal core of H. The paper consists of the following three sections:In section one: we introduce some backgrounds of our research.In section two:we introduce some basic concepts, and lemma as used in this paper.In section three: Use the properties of core(m)-groups, show some structure of core(m)-groups.The following conclusions are derived:Theorem3.1Let G be a core(1)-group, and G is not a super solvable group, then G has a normal abelian subgroup of index divisible2pq or4q.Theorem3.2Let G be a core(1)-group, and G is a super solvable group, then G has a normal abelian subgroup of index divisible16p or2pq2.