自同构群的阶为2pq^2的一类群

Groups with automorphism group of order 2pq^2

给出了自同构群的阶为2pq2的一类群的分类,其中p和q是任意不同的奇素数,且q大于3。得到的主要结果是:若G不为无非平凡交换直因子的非幂零群,且|Aut(G)|=2pq2(p,q是奇素数,p≠q,q>3),则G同构于C(2p+1)3,C2pq2+1,C2×C(2p+1)3,C2×C2pq2+1之一。

This paper classifies the groups with automorphism group of order 2pq2,where p and q are different odd primes,and q is a prime more than 3.The authors have obtained the following result：Let G be not a non-nilpotent group without non-commutative direct factor,and-Aut（G）-=2pq2（p,q are different odd primes,p≠q,q3）,then,G is one of the following groups：C（2p＋1）3,C2p q2＋1,C2×C（2p＋1）3,C2×C2p q2＋1.