With the help of group theory and number theory , analyzing the character of the defining relations of p- groups (where p is an odd prime ) and the properties of automorhism and other properties such as the properties of metabelian,regularity,p-commutativity and some properties of equivalence,by solving equations of congruence .
本文综合运用群论和数论的知识，通过分析群的定义关系和同构性质以及其他性质如正则性，亚交换性，p-交换性，用解同余方程的方法，得到了[4]中p~6阶群的Φ_(13)，Φ_(24)，Φ_(25)，Φ_(26)族的所有p-群的自同构群的阶，其中p是奇素数。