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Doubly transitive permutation groups with abelian stabilizers

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Summary

We prove that any doubly transitive permutation group with abelian stabilizers is the group of linear functions over a suitable field. The result is not new: for finite groups it is well known, for infinite groups it follows from a more general theorem of W. Kerby and H. Wefelscheid on sharply doubly transitive groups in which the stabilizers have finite commutator subgroups. We give a direct and elementary proof.

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Authors and Affiliations

  1. Eötvös University, Múzeum körút 6-8, H-1088, Budapest, Hungary

    Gy. Károlyi & S. J. Kovács

  2. Hungarian Academy of Sciences, Pf. 127, H-1364, Budapest, Hungary

    P. P. Pálfy

Authors
  1. Gy. Károlyi
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  2. S. J. Kovács
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  3. P. P. Pálfy
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Károlyi, G., Kovács, S.J. & Pálfy, P.P. Doubly transitive permutation groups with abelian stabilizers. Aeq. Math. 39, 161–166 (1990). https://doi.org/10.1007/BF01833147

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  • DOI: https://doi.org/10.1007/BF01833147

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