关于单K_3-群L_3(3)和U_3(3)

On Simple K_3-Groups L_3(3) and U_3(3)

设G为有限群,o1(G)表示G中最高阶元素的阶。用极少的数量刻画有限单群是单群刻画领域中一个有趣的课题。本文只用群的阶及最高阶元素的阶刻画了单K3-群L3(3)和U3(3),即证明了:设G为有限群,M为单K3-群L3(3)和U3(3),则G≈M当且仅当|G|=|M|,且o1(G)=o1(M)。

Let G be a finite group,o1（G）denote the largest element order G.It is an interesting topic to characterize a finite simple group by using.In his paper,we characterizes simple K3-groups L3（3）and U3（3） only by using Gand o1（G）,that is to say,we prove that： Let G be a finite group M be simple K3-group L3（3）and U3（3）.Then G≈M if and only if ｜G｜=｜M｜,and o1（G）=o1（M）.