李型单群C_n(3)的谱刻画

Recognition of simple groups C_n(3) of Lie type by their spectrum

为找到有限单群所特有的算术性质,根据素图的连通分支,结合素图的连接标准,利用元素阶的集合,刻画了素图非连通的李型单群Cn(3)(其中n≠2),结果表明:对有限群G,若G与Cn(3)的元素的阶的集合相同,则G与Cn(3)同构,从而也证实了Kondratiev的猜想对李型单群Cn(3)也是成立的.该成果对有限群的数量刻画具有一定的参考价值和指导意义.

In order to find the special arithmetic properties of finite simple groups,according to the connected component of prime graph and the adjacency criterion for prime graph,the simple groups Cn(3)(where n≠2) of Lie type with disconnected prime graph are recognized by their element orders.The study found that every finite group G with the same set of element orders as Cn(3) is isomorphic to Cn(3).Also,Kondratiev's conjecture is true to simple groups Cn(3).The study has a reference value and some significance to the recognizability of finite groups.