Self-Conjugate Permutable Subgroups And Nearly Normal Subgroups

The structure of a group closely relates to the characters of subgroups. We can get groups which have different compositions through researching the characters of different subgroups. In this paper, we mainly study p-nipotent groups through self-conjugate permutable subgroup and nearly normal subgroup. Let G be a finite group. A subgroup H of a group G is called self-conjugate permutable subgroup if HHx=HxH implies H=Hx for each x in G. A subgroup H of a group G is called nearly normal subgroup if there exists another subgroup N(?)G, which satisfied HN(?)G and H∩N< G.The first chapter mainly introduces researching background of correlative prob-lems and some definitions and theorems; The second chapter introduces the influ-ence of some special character of subgroups for the finite group; the third chapter discusses the p-nipotency of finite groups through the self-conjugate permutability of cyclic subgroups of order p and 4; the forth chapter discusses the p-nipotency of finite groups through some nearly normal subgroups.