Finite Abelian Group with Automorphism Group for Order 2tp2（p is odd prime）

The structures of finite Abelian group G with automorphism group A(G) for the order 2tp2(t=1,2,3 p is odd prime)are discussed.According to the order of automorphism group of finite abelian group and the character of finite abelian group,the following results are obtained:G has 4 types when t=1;G has 12 types when t=2;G has 21 types when t=3.