Thompson's conjecture for Lie type groups E_7(q)  

作　　者：XU MingChun SHI WuJie 

机构地区：[1]School of Mathematics, South China Normal University [2]Department of Mathematics, Chongqing University of Arts and Sciences

出　　处：《Science China Mathematics》2014年第3期499-514,共16页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11171118,10961007 and 11171364);the Innovation Foundation of Chongqing University(Grant No.KJTD201321)

摘　　要：In this article, we prove a conjecture of Thompson for an infinite class of simple groups of Lie type ET（q）. More precisely, we show that every finite group G with the properties Z（G） = 1 and cs（G） = cs（ET（q）） is necessarily isomorphic to ET（q）, where cs（G） and Z（G） are the set of lengths of conjugacy classes of G and the center of G respectively.In this article,we prove a conjecture of Thompson for an infinite class of simple groups of Lie type E7(q).More precisely,we show that every finite group G with the properties Z(G)=1 and cs(G)=cs(E7(q))is necessarily isomorphic to E7(q),where cs(G)and Z(G)are the set of lengths of conjugacy classes of G and the center of G respectively.

关 键 词：simple group minimal normal subgroup conjugacy classes CENTRALIZER 

分 类 号：O152.1[理学—数学] TP392[理学—基础数学]