Lifting of Outer Actions of Groups  

作　　者：Fang ZHOU He Guo LIU 

机构地区：[1]Department of Mathematics, Taiyuan Normal University, Taiyuan 030012, P. R. China [2]Department of Mathematics, Hubei University, Wuhan 430062, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2010年第9期1693-1700,共8页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China (Grant No. 10671058)

摘　　要：Let G and N be arbitrary groups. In this paper, we construct an associated group extension εx of N/Z（N） by G for any group homomorphism X ： G → Out N, and prove that X can be lifted to a group action, that is, a group homomorphism from G to Aut N, if and only if the extension εx splits. Furthermore we obtain an explicit description for all such lifting homomorphisms and the number of its conjugacy classes, and give an application of the lifting technique of outer actions to the theory of group extensions.Let G and N be arbitrary groups. In this paper, we construct an associated group extension εx of N/Z（N） by G for any group homomorphism X ： G → Out N, and prove that X can be lifted to a group action, that is, a group homomorphism from G to Aut N, if and only if the extension εx splits. Furthermore we obtain an explicit description for all such lifting homomorphisms and the number of its conjugacy classes, and give an application of the lifting technique of outer actions to the theory of group extensions.

关 键 词：Outer action group extension LIFTING 

分 类 号：O157[理学—数学] O152.1[理学—基础数学]