Finite Projective Planes

Details Finite Projective Planes Finite Projective Planes

2006-11-16

arxiv.org/abs/math/0611492v1

Mathematics

General Mathematics

16 pages

Scientific paper

This paper addresses the following question: For the existence of a finite projective plane of order n why n should be a prime power? We show that the problem of existence of a finite projective plane of order n can be linked up with the existence of a sharply 2-transitive subgroup of Sn (the group of permutations on n symbols) of order n(n-1) containing a regularly normal subgroup of order n. We show that the finite projective plane of order n exists if and only if a sharply 2-transitive subgroup of Sn of order n(n-1) containing a regularly normal subgroup of order n exists. It is clear from known results [1], [2] that when such a group exists n is a prime power. We thus settle the problem of the nonexistence of finite projective planes when their order is not a prime power.

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