一类广义超特殊p-群的因子分解数

Factorization Number of a Class of Generalized Extraspecial p-groups

设G是一个有限群,A,B是G的两个子群,若G=AB,则称G被A和B因子分解.设G是如下的一类广义超特殊p-群,G=<x,y,z|x^p=y^p=z^(p^m)=1,[x,z]=[y,z]=1,[x,y]=z^(p^(m-1))>,m≥1,则G的因子分解数被确定.

Let G be a finite group, A and B be two subgroups of G. If G=AB, then G is said to be factorized by A and B. Let G be a generalized extraspecial p-group as follows, G=m 〈x,y,z｜xp=yp=zpm=1,[x,z]=[y,z]=1,[x,y]=z p m-1〉,m≥ 1, then the factorization number of G is determined.