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    Symmetric representation of the elements of the Conway group .0

    Fairbairn, Ben and Curtis, R. (2009) Symmetric representation of the elements of the Conway group .0. Journal of Symbolic Computation 44 (8), pp. 1044-1067. ISSN 0747-7171.

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    In this paper we represent each element of the Conway group .0 as a permutation on 24 letters from the Mathieu group M24, followed by a codeword of the binary Golay code (which corresponds to a diagonal matrix taking the value -1 on the positions of the codeword and 1 otherwise), followed by a word of length at most 4 in a highly symmetric generating set. We describe an algorithm for multiplying elements represented in this way, that we have implemented in Magma. We include a detailed description of L4, the sets of 24 mutually orthogonal 4-vectors in the Leech lattice L. often referred to as frames of reference or crosses, as they are fundamental to our procedure. In particular we describe the 19 orbits of M24 on these crosses.


    Item Type: Article
    Keyword(s) / Subject(s): Conway group, Leech lattice, symmetric generation
    School: Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
    Depositing User: Ben Fairbairn
    Date Deposited: 03 Jan 2013 12:54
    Last Modified: 09 Aug 2023 12:32


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