Transitive projective planes and 2-rank

Nick Gill

Transitive projective planes and 2-rank

Group Theory 2008-03-06 v2 Combinatorics

Authors: Nick Gill

Abstract

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 $\mathcal{P}$ .

Keywords

group actions wreath product of groups algebraic group actions

Cite

@article{arxiv.0711.4459,
  title  = {Transitive projective planes and 2-rank},
  author = {Nick Gill},
  journal= {arXiv preprint arXiv:0711.4459},
  year   = {2008}
}

Comments

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

Transitive projective planes and 2-rank

Abstract

Keywords

Cite

Comments

Related papers