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Locally elusive classical groups

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Abstract

Let G be a transitive permutation group of degree n with point stabiliser H and let r be a prime divisor of n. We say that G is r-elusive if it does not contain a derangement of order r. The problem of determining the r-elusive primitive groups can be reduced to the almost simple case, and the purpose of this paper is to complete the study of r-elusivity for almost simple classical groups. Building on our earlier work for geometric actions of classical groups, in this paper we handle the remaining non-geometric actions where H is almost simple and irreducible. This requires a completely different approach, using tools from the representation theory of quasisimple groups.

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Authors and Affiliations

  1. School of Mathematics, University of Bristol, Bristol, BS8 1TW, UK

    Timothy C. Burness

  2. Centre for the Mathematics of Symmetry and Computation, Department of Mathematics and Statistics, The University of Western Australia, Crawley, WA, 6009, Australia

    Michael Giudici

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  1. Timothy C. Burness
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  2. Michael Giudici
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Correspondence to Timothy C. Burness.

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Burness, T.C., Giudici, M. Locally elusive classical groups. Isr. J. Math. 225, 343–402 (2018). https://doi.org/10.1007/s11856-018-1663-7

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  • DOI: https://doi.org/10.1007/s11856-018-1663-7

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