Transitive permutation groups where nontrivial elements have at most two fixed points

Motivated by a question on Riemann surfaces, we consider permutation groups that act nonregularly, such that every nontrivial element has at most two fixed points. We describe the permutation groups with these properties and give a complete, detailed classification when the group is simple.

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Bibliographic Details
Published in:Journal of pure and applied algebra 2015-04, Vol.219 (4), p.729-759
Main Authors: Magaard, Kay, Waldecker, Rebecca
Format: Article
Language:English
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Description
Summary:Motivated by a question on Riemann surfaces, we consider permutation groups that act nonregularly, such that every nontrivial element has at most two fixed points. We describe the permutation groups with these properties and give a complete, detailed classification when the group is simple.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2014.04.027