This paper disscusses the types of finite Abelian groups G with |A(G)|=2p~n, 2~2p~n, 2~3p~n.

• 本文是[1]、[2]的继续,利用群G的自同构群A(G)来刻划群G的构造,给出了|A(G)|=2p~n,2~2p~n,2~3p~n的有限Abel群G的全部类型。