A character-theory-free characterization of the simple groups M_{11} and L<sub>3</sub>(3)


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.

DOI Code: 10.1285/i15900932v10supn2p283

Classification: 20D05; 20D08

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