素数幂次本原置换群的一个简明刻画

A Description of Primitive Permutation Groups of Prime Power Degree

一般置换群的研究可以通过轨道归结为传递置换群的研究,而传递置换群的研究又可以通过非本原块转化为本原群的研究.O′Nan-Scott定理描述了本原置换群的结构,但是刻画特殊次数的本原置换群仍然是一个非常有趣的问题,为此对素数幂次的本原置换群给出一个清晰明了的刻画.

The study of general permutation groups is often reduced to the transitive case,and the transitive case can usually be reduced to the primitive case.Due to the O′Nan-Scott Theorem,the structure of finite primitive permutation groups is clear,but finding explicit description of finite primitive permutation groups of special degree is always an interesting problem.In this paper we present such a list for finite primitive permutation groups of prime power degree.