p6阶若干家族群的自同构群的阶*

目的确定p~6阶群Φ_(31)到Φ_(35)家族中所有群的自同构群阶。方法在1980年Rodney James文章中对p~6阶群的分类基础上,运用数论与群论知识并结合矩阵方程的方法。结果与结论给出了p~6阶群Φ_(31)到Φ_(35)家族所有群的自同构群的阶。

The orders of automorphism groups of some families of groups of order p6

Purposes—To determine the orders of automorphism groups of the groups of order p6 from the thirty‐first family to thirty‐five family .Methods—Based on the classification of groups of or‐der p6 in the paper by Rodney James in 1980 ,number theory ,group theory knowledge and the method of matrix equation are adopted to accomplish the aforesaid purpose .Results and Conclusion— The or‐ders of automorphism groups of the groups of order p6 from the thirty‐first family to thirty‐five family are given .