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Embeddings of the groupL(2,13) in groups of lie typeE 6

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Abstract

In this paper we show there is exactly one conjugacy class of subgroups ofE 6(ℂ) isomorphic toL(2, 13) with each of the characters 13+14 and 1+12+14 on a 27-dimensional module forE 6. The one with character 13+14 is a subgroup of the irreducible closed subgroup of typeG 2. There is a unique conjugacy class for each of the three algebraic conjugate characters 1+12+14. Our arguments have applications to fields of characteristic prime to |L(2, 13)|.

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Authors and Affiliations

  1. Dept. AM, CWI, Kruislaan 413, 1098 SJ, Amsterdam, The Netherlands

    Arjeh M. Cohen

  2. Caltech, Sloan Lab, 91125, Pasadena, CA, USA

    David B. Wales

Authors
  1. Arjeh M. Cohen
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  2. David B. Wales
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Dedicated to John Thompson for his keen interest in broad areas of mathematics and in mathematicians

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Cohen, A.M., Wales, D.B. Embeddings of the groupL(2,13) in groups of lie typeE 6 . Israel J. Math. 82, 45–86 (1993). https://doi.org/10.1007/BF02808108

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  • DOI: https://doi.org/10.1007/BF02808108

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