Abelian quotients and orbit sizes of linear groups  

作　　者：Thomas Michael Keller Yong Yang 

机构地区：[1]Department of Mathematics,Texas State University,San Marcos,TX 78666,USA [2]Key Laboratory of Group and Graph Theories and Applications,Chongqing University of Arts and Sciences,Chongqing 402160,China

出　　处：《Science China Mathematics》2020年第8期1523-1534,共12页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11671063);a grant from the Simons Foundation(Grant No.280770 to Thomas M.Keller);a grant from the Simons Foundation(Grant No.499532 to Yong Yang)。

摘　　要：Let G be a finite group,and let V be a completely reducible faithful finite G-module(i.e.,G≤GL(V),where V is a finite vector space which is a direct sum of irreducible G-submodules).It has been known for a long time that if G is abelian,then G has a regular orbit on V.In this paper we show that G has an orbit of size at least|G/G′|on V.This generalizes earlier work of the authors,where the same bound was proved under the additional hypothesis that G is solvable.For completely reducible modules it also strengthens the 1989 result|G/G′|<|V|by Aschbacher and Guralnick.

关 键 词：abelian quotients orbits of group actions linear groups 

分 类 号：O152.1[理学—数学]