非正规子群链长为3的有限p群

Finite p-Groups Whose Length of Chain of Nonnormal Subgroups is 3

设G为有限非Dedekind p群,则■H≤G,使得H■G.设p> 2,对于非正规子群链长为3的有限p群,本文主要分类了chn(G)=3且非正规子群的阶恰为pm,pm+1,pm+2(m≥3)的有限p群,记这类群为P群.

Suppose that G is a finite non-Dedekind p-group.Let H is a non-normal subgroups of G.Let p>2.For the finite p-groups Whose Length of Chain of Nonnormal Subgroups is 3,this paper mainly groups G such that m(G)≥3,M(G)-m(G)=2 and chn(G)=3.we denoted such this p-groups as P groups.