Vol. 39, No. 1, 1971

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ISSN: 0030-8730
On rank 3 projective planes

Michael Joseph Kallaher

Vol. 39 (1971), No. 1, 207–214
Abstract

One of the unsolved problems in the theory of projective planes is the following: Is every finite projective plane with a transitive collineation group desarguesian? This problem is investigated under the additional hypothesis that the group has rank 3. It is proven that if a projective plane 𝒫 of order n > 2 has a rank 3 collineation group then 𝒫 is nondesarguesian and either (i) n is odd and n = m4, or (ii) n is even and n = m2 with m = 0( mod 4).

Mathematical Subject Classification
Primary: 50D30
Milestones
Received: 12 January 1971
Published: 1 October 1971
Authors
Michael Joseph Kallaher