自同构群是循环群被交换群扩张的有限群

Finite Groups with Atitomorphism Group an Extension of a Cyclic Group by anAbelian Group

设Ｃ是有限群，ＡｕｔＧ＝ＡＢ，，Ａ是交换群且每Ｓｙｌｏｗ子群的秩≤２，Ｂ是循环群，本文得出了Ｇ的结构，特别地，证明了ＡｕｔＧ是秩≤２的交换群时，Ｇ循环。

Let G be A finite group,AutG=HS,(|H|,|S|)=1,H is a Abeliangroup with all Sylow subgroups generated by at most two elements,S is a cyclic group. In thispaper we find out all such fiuite groups G. Especially we come to the conclusion;‘IF Aut G is aAbelian group generated by at most two elements,then G is cyclic.’