特殊线性群L3（37）和L2（113）的最短共轭类刻画

Characterization of the Projective Special Linear Group of L3 （37） and L2 （113） by Their Smallest Conjugacy Class Size

利用群的数量特征刻画有限单群很有意义。利用群的阶及最短共轭类长刻画了素因子个数为6和7的两个有限非交换单群。证明了特殊线性群L3(37)和L2(113)是可用群的阶及最短共轭类长来刻画的。

It is interesting to characterize finite simple groups by their quantitative characteristics. In this paper, the authors have characterized two finite nonabelian simple groups with 6 and 7 prime factors by their orders and their smallest conjugacy class sizes greater than one. More precisely, we show that L3 （37） and L2 （113 ） can be characterized by their orders and their smallest conjugacy class sizes greater than one.