2015/09/22 by Michael Tait, Tait, Michael
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO
paper · pdf · doi:10.48550/arxiv.1509.06587
arxiv created 2015/10/20 · arxiv updated 2015/10/21
A conjecture widely attributed to Neumann is that all finite non-desarguesian projective planes contain a Fano subplane. In this note, we show that any finite projective plane of even order which admits an orthogonal polarity contains a Fano subplane. The number of planes of order less than n previously known to contain a Fano subplane was O(log n), whereas the number of planes of order less than n that our theorem applies to is not bounded above by any polynomial in n.