关于2~np^2(n≥3)阶群构造的一个注记

A Note on the Structure of Groups of Order 2~np^2(n≥3)

利用Sylow2-子群是二面体群、半二面体群、广义四元数群的特殊结构,通过群的扩张理论,利用群作用的方法,解决了Sylow p-子群自正规化。Sylow2-子群是二面体群,半二面体群或广义四元数群的2np2阶群的分类。

In this paper, by using the special structures of some groups which are dihedral groups, or semi -dihedral groups, or quaternion groups, and some theorems in extension of groups, we obtain the classification of groups of order 2np2, Sylow p-subgroups of which are self-normalizer, and Sylow 2-subgroups are dihedral or semi-dihedral or quaternion groups.