一类齐次循环2-群的无不动点自同构  

Fixed-Point-Free Automorphisms of a Kind of Homocyclic 2-Groups

作　　者：李向东[1] 靳平[1] 

机构地区：[1]山西大学数学科学学院,太原030024

出　　处：《太原科技大学学报》2008年第6期467-468,共2页Journal of Taiyuan University of Science and Technology

摘　　要：研究了齐次循环2-群G=G2n×C2n(n≥1)的无不动点自同构,得到了G的自同构为无不动点自同构的一个充要条件,并证明了G的所有无不动点自同构的集合恰为O2(AutG)在AutG中两个不同的陪集之并。In this paper, fixed-point-free automorphisms of homocyclic 2-groups G=G2n×G2n fore n ≥ 1 are studied. A necessary and suffcient condition for an automorphism of G to be fixed-point-free is obtained. And it is proved that the set of fixed-point-free automorphisms of G is precisely a union of two different cosets of O2 （Aut G） in Aut G.

关 键 词：齐次循环2- 自同构群 无不动点自同构 

分 类 号：O152.1[理学—数学]