Transitive projective planes and 2-rank

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Gill, Nick
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Suppose that a group $G$ acts transitively on the points of a non-Desarguesian plane, $\mathcal{P}$. We prove first that the Sylow 2-subgroups of $G$ are cyclic or generalized quaternion. We also prove that $\mathcal{P}$ must admit an odd order automorphism group which acts transitively on the set of points of $\mathcal{P}$.
Comment: 29 pages. This version is significantly expanded (9 extra pages). Proofs which were formerly omitted or only sketched are now given in detail. In addition the exposition is (hopefully) much more readable
Keywords
Mathematics - Group Theory, Mathematics - Combinatorics, 20B25, 51A35
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