On rank 5 projective planes

Otto Bachmann

International Journal of Mathematics and Mathematical Sciences, 1984, vol. 7, 1-12

Abstract:

In this paper we continue the study of projective planes which admit collineation groups of low rank (Kallaher [1] and Bachmann [2,3]). A rank 5 collineation group of a projective plane ℙ of order n ≠ 3 is proved to be flag-transitive. As in the rank 3 and rank 4 case this implies that is ℙ not desarguesian and that n is (a prime power) of the form m 4 if m is odd and n = m 2 with m ≡ 0 mod 4 if n is even. Our proof relies on the classification of all doubly transitive groups of finite degree (which follows from the classification of all finite simple groups).

Date: 1984
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:612463

DOI: 10.1155/S0161171284000351

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