具有给定共轭类长的有限群

Finite Groups with the Given Length of Conjugacy Classes

通过有限群G的共轭类长集合cs(G)来刻画有限群A6和S6,得到如下结论:如果cs(G)=cs(G)={1,p3.r,p.q2.r,p3.q2,q2.r},则GA6;如果cs(G)={1,q.r,p3.r,q2.r,p.q2.r,p3.q.r,p4.q2},则GS6.

This paper characterizes the groups A6 and S6 by the set of size of conjugacy classes,and gets the following results： If cs（G）=cs（G）={1,p3·r,p·q2·r,p3·q2,q2·r},then G≌A6;If cs（G）={1,q·r,p3·r,q2·r,p·q2·r,p3·q·r,p4·q2},则G≌S6.