自同构群的阶为2~tp^2q(t=1,2,3)的有限Abel群G

STRUCTURE OF FINITE ABELIAN GROUP WITH AUTOMORPHISM GROUP OF ORDER 2~tp^2q(t=1,2,3)

本文研究了自同构群A(G)阶为2tp2q(t=1,2,3)(p,q为不同的奇素数)的有限Abel群G的构造.利用有限Abel群G的自同构群的阶和有限Abel群的性质,获得以下结果:当t=1时,G最多有6型;当t=2时,G最多有32型;当t=3时,G最多有82型.

This article discusses the structure of finite abelian group G with automorphism group A（G） of order 2^tp^2q（t=1,2,3）（p,q are different prime）.According to order of automorphism group of finite abelian group and character of finite abelian group,we obtain the following results：G has 6 types when t=1;G has 32 types when t=2;G has 82 types when t=3.