Doubly transitive permutation groups with abelian stabilizers |
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Authors: | Gy Károlyi S J Kovács P P Pálfy |
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Institution: | (1) Eötvös University, Múzeum körút 6-8, H-1088 Budapest, Hungary;(2) Hungarian Academy of Sciences, Pf. 127, H-1364 Budapest, Hungary |
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Abstract: | 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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Keywords: | Primary 20B22 |
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