自同构群阶为4p_1p_2···p_n的有限群

Finite groups whose automorphism groups have order 4p_1p_2· · ·p_n

设G是有限群,m是已知正整数,求解方程|Aut(G)|=m中的有限群G是一个难度很大的问题.此课题的系统研究始于上世纪70年代末.后来陆续有包括本文作者在内的研究者对于m是一些特殊的数时方程的求解问题进行了研究,目前已经取得了一系列的结果.本文在过去研究的基础上研究|Aut(G)|=4p1p2···pn的求解问题,并求出了全部有限群,推广了杜妮和李世荣的结果.

Let G be a finite group, m a positive integer. Solving the equation ｜Aut（G）｜ = m is a difficult topic. The earliest research on this topic appeared in 1979. Afterwards, there is a series of solutions for special numbers m given by mathematicians including the authors of this paper. In this paper, the authors solve the equation ｜Aut（G）｜ =4p1p2 …… pn and find out all finite groups G, which is a generalization of results given by Du and Li.