摘要
确定了每个非分裂有限亚循环2-群的自同构群的结构及阶数。同时完成了有限亚循环p-群的自同构群的计算工作。
In this paper,the structure and the order of the automorphism group of each nonsplit metacyclic 2-group are determined.This completes the work of computing automorphism groups for metacyclic p-groups.
引文
[1] ZASSENHAUS H J.The theory of groups[M].Second edition,Chelsea,New York:Dover Pubns,1956.
[2] BIDWELL J N S,CURRAN M J.The automorphism group of a split metacyclic p-group[J].Archiv der Mathematik,2006(87):488-497.
[3] CURRAN M J.The automorphism group of a split metacyclic 2-group[J].Arch Math,2007(89):10-23.
[4] CURRAN M J.The automorphism group of a nonsplit metacyclic p-group[J].Arch Math,2008(90):483-489.
[5] 刘海林,伍星,于雪,et al.有限亚循环群的自同构群的可解性[J].广西师范学院学报(自然科学版),2017(2):24-27.
[6] CHEN H M,XIONG Y S,ZHU Z J.Automorphism of metacyclic groups[J].Czech Math J,2018(143):803-815.
[7] KING B W.Presentations of metacyclic groups[J].Bull.Austral.Math.Soc,1973(8):103-131.
[8] 朱德高,左国新.(广义)四元数群的自同构群及其全形[J].数学物理学报,2005,25(1):79-83.
[9] IRELAND K,ROSEN M.A classical introduction to modern number theory[M].Graduate Texts in Mathematics,Vol.84,2nd edtion,New York:Springer-Verlag,1990.
[10] BROWN K S.Cohomology of groups[M].Graduate Texts in Mathematics,Vol.87,New York,Heidelberg,Berlin:Springer-Verlag,1982.