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Transitive projective planes and insoluble groups


Author: Nick Gill
Journal: Trans. Amer. Math. Soc. 368 (2016), 3017-3057
MSC (2010): Primary 20B25, 51A35
Published electronically: January 6, 2016
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Abstract: Suppose that a group $ G$ acts transitively on the points of $ \mathcal {P}$, a finite non-Desarguesian projective plane. We prove that if $ G$ is insoluble, then $ G/O(G)$ is isomorphic to $ \mathrm {SL}_2(5)$ or $ \mathrm {SL}_2(5).2$.


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Additional Information

Nick Gill
Affiliation: Department of Mathematics, The Open University, Walton Hall, Milton Keynes, MK7 6AA, United Kingdom
Address at time of publication: Department of Mathematics, University of South Wales, Treforest, CF37 1DL, United Kingdom
Email: nick.gill@southwales.ac.uk

DOI: https://doi.org/10.1090/tran/6366
Received by editor(s): January 28, 2013
Received by editor(s) in revised form: December 20, 2013, and December 21, 2013
Published electronically: January 6, 2016
Article copyright: © Copyright 2016 American Mathematical Society