A character-theory-free characterization of the simple groups $M_{11}$ and $L₃(3)$

Abstract

The existing proofs of the characterization of me Mathieu group $M_{11}$, by the centralizer of one of its involutions make heavy use of the theory of group characters. There was a strong feeling that in small cases like this character theory was absolutely indispensable to make up for the poor local structure faced with in such situations. Up to now, the characterization of $M_{11}$ has served as an illustration of the power of the theory of exceptional characters. Here, in the course of the post-classification effort to simplify proofs, we show that $M_{11}$ can be treated in a completely elementary and group theoretical way while carrying out each step of the argument in detail.