自同构群的阶为2~6p^2的有限Abel群

The finite Abelian groups with automorphism groups of degree 2~6p^2

设p是奇素数,G是有限Abel群,A(G)是G的自同构群.运用初等数论方法证明了:当|A(G)|=26p2时,如果p≠3,5或17,则G至多有20种类型.

Let p be an odd prime,let G be a finite Abelian group,and let A（G） denotes the automorphism group of G.In this paper,using method of elementary number theory,it is proved that if ｜A（G）｜=26p2,where p≠ 3,5 or 17,then G has at most 20 types.