Transitive projective planes and insoluble groups

Details Transitive projective planes and insoluble groups Transitive projective planes and insoluble groups

2009-03-19

arxiv.org/abs/0903.3302v2

Mathematics

Group Theory

44 pages. This version is greatly expanded; in particular there is a lengthy treatment of subgroups of $GL(n,q)$. Some errors

Scientific paper

Suppose that a group $G$ acts transitively on the points of $\mathcal{P}$, a
finite non-Desarguesian projective plane. We prove first that the Sylow
2-subgroups of $G$ are cyclic or generalized quaternion; we then prove that if
$G$ is insoluble then $G/O(G)$ is isomorphic to $SL_2(5)$ or $SL_2(5).2$.

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