Who conjectured that a transitive projective plane is Desarguesian? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-20T20:30:49Z http://mathoverflow.net/feeds/question/66632 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/66632/who-conjectured-that-a-transitive-projective-plane-is-desarguesian Who conjectured that a transitive projective plane is Desarguesian? gordon-royle 2011-06-01T07:06:44Z 2011-06-04T00:04:12Z <p>The only known finite projective plane with a transitive automorphism group is the Desarguesian plane \$PG(2,q)\$ and it seems likely that there are no others, although this is not (quite) proved.</p> <p>However all the papers that I have seen dealing with this problem or variants of this problem say things like "It is a longstanding conjecture that a transitive projective plane is Desarguesian" or "It has been conjectured that ..." and none of them actually say who made the original conjecture. </p> <p>I've looked in Kantor's papers on flag-transitive planes, Dembowski's book on Finite Geometries, Ostrom and Wagner's paper proving that planes with <em>doubly</em> transitive groups are Desarguesian and Higman and McLaughlin's paper on ABA groups.</p> <p>So is the conjecture folklore? Or can anybody point me to an explicit reference?</p> <p>EDIT: Question has been up for a few days without answer so I'm giving up and assigning the result to "folklore". In the meantime, I've written a blog post about it for posterity: <a href="http://symomega.wordpress.com/2011/06/03/an-elusive-conjecture/" rel="nofollow">http://symomega.wordpress.com/2011/06/03/an-elusive-conjecture/</a></p>