Suzuki-Ree群的自同构群的阶分量刻画

Automorphism Groups of Suzuki-Ree Groups Can Be Characterized by Their Order Components

在《数学学报》2013年第56卷第4期中,"Suzuki-Ree群的自同构群的一个新刻画"一文证明了Aut(~2^F4(q)),q=2^f和Aut(2^G2(q)),q=3^f,可由其阶分量刻画,其中f=3^s,s为正整数.本文证明了Aut(2^B2(q)),q=2^f和Aut(2G2(q)),q=3^f,也可由其阶分量刻画,其中f为奇素数.结合二者得到结论:Suzuki-Ree单群的所有的素图不连通的自同构群皆可由其阶分量刻画.

The paper[A new characterization of automorphism groups of Suzuki-Ree groups, Acta Math. Sin., Chin. Ser., 2013, 56(4), 545-552] proved that Aut(2F4(q)), q=2^f and Aut(2G2(q)), q=3^f can be characterized by their order components, where f=3s, s is a positive integer. We proved that Aut(2B2(q)), q=2^f and Aut(2G2(q)), q=3f also can be characterized by their order components, where f is a odd prime. Combining both, we can obtain that the automorphism groups of the Suzuki-Ree simple groups whose prime graphs are not connected can be characterized by their order components.