Artin单群的一种刻画

A Characterization of Artin Simple Groups

设L是一个有限单群.若存在素数p,使得p||L|且p>|L|1/3,则称L是一个Artin单群.Brauer和Reynolds在1958年给出了Artin单群的完全分类:PSL2(p),p>3是一个素数,和PSL2(p-1),p>3为一个Fermat素数.不借助于有限单群分类定理,本文利用群阶和一个共轭类长刻画了Artin单群,作为推论得出了Thompson猜想对Artin单群成立.

Let L be a finite simple group.If it exists a prime p such that p||L|and p>|L|1/3,then L is called an Artin simple group.In 1958,Brauer and Reynolds classified Artin simple groups,which are PSL2(p)where p>3 is a prime,and PSL2(p-1)where p>3 is a Fermat prime.Without the help of classification theorem of finite simple groups,the authors characterize the Artin simple groups by their order and one conjugacy class length in this short note.This work implies that Thompson’s conjecture holds for Artin simple groups.