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Monomial modular representations and symmetric generation of the Harada–Norton group

✍ Scribed by John N. Bray; Robert T. Curtis

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
283 KB
Volume
268
Category
Article
ISSN
0021-8693

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✦ Synopsis

This paper is a sequel to Curtis [J. Algebra 184 (1996) , where the Held group was constructed using a 7-modular monomial representation of 3 • A 7 , the exceptional triple cover of the alternating group A 7 . In this paper, a 5-modular monomial representation of 2 • HS: 2, a double cover of the automorphism group of the Higman-Sims group, is used to build an infinite semi-direct product P which has HN, the Harada-Norton group, as a 'natural' image. This approach assists us in constructing a 133-dimensional representation of HN over Q( √ 5 ), which is the smallest degree of a 'true' characteristic 0 representation of P. Thus an investigation of the low degree representations of P produces HN. As in the Held case, extension to the automorphism group of HN follows easily.

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