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Further elementary techniques using the miracle octad generator

  • R. T. Curtis
Extract

In this paper we describe various techniques, some of which are already used by devotees of the art, which relate certain maximal subgroups of the Mathieu group M24, as seen in the MOG, to matrix groups over finite fields. We hope to bring out the wealth of algebraic structure underlying the device and to enable the reader to move freely between these matrices and permutations. Perhaps the MOG was mis-named as simply an “octad generator”; in this paper we intend to show that it is in reality a natural diagram of the binary Golay code.

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References
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1.Benson, D. J., The Construction of J4 (Ph.D. thesis, Cambridge, 1980).
2.Conway, J. H., Three lectures on exceptional groups, in Finite Simple Groups (eds. Powell, M. B. and Higman, G., Academic Press, London, Orlando and New York), 215247.
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7.Curtis, R. T., On subgroups of 0, II local structure, J. Algebra 63 (1980), 413434.
8.Curtis, R. T., Eight octads suffice, J. Combin. Theory Ser. A 36 (1984), 116123.
9.Todd, J. A., A representation of the Mathieu group M 24 as a collineation group, Anc. Mat. Para Appl. Ser. IV 71 (1966), 199238.
10.Wilson, R. A., The maximal subgroups of Conway's group 2, J. Algebra 84 (1983), 107114.
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Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
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