Abstract
In this paper we show how to construct 4370 x 4370 matrices over GF(2), generating Fischer's {3,4}transposition group B, popularly known as the Baby Monster. This for the first time gives a construction which permits effective calculations to be performed in this very large simple group. We use this to give a new existence proof, and describe briefly applications to subgroup structure, geometry, 2-modular characters, and genus actions.
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