自同构群的阶为2^tpq(1≤t≤3)的有限Abel群G

Finite Abelian Group with Automorphism Group for Order 2^tpq(1≤t≤3)

本文利用有限Abel群G的性质和它的自同构群的阶,讨论了自同构群A(G)的阶为2tpq(1≤t≤3)的有限Abel群G的构造。得出以下结果:当t = 1时,G最多有6型;当t = 2时,G最多有22型;当t = 3时,G最多有49型。

In this paper,according to the character of finite Abelian group G and the order of automorphism group of it,the structure of finite Abelian group G with automorphism group for the order 2tpq(1≤t≤3) is discussed.The following results are obtained:G has 6 types when t=1;G has 22 types when t=2;G has 49 types when t=3.