Proof of the prime power conjecture for projective planes of order 𝑛 with abelian collineation groups of order 𝑛²-Reference-Cited by-同舟云学术

Proof of the prime power conjecture for projective planes of order 𝑛 with abelian collineation groups of order 𝑛²

Published:2001-12-20 Issue:5 Volume:130 Page:1473-1476
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Blokhuis Aart,Jungnickel Dieter,Schmidt Bernhard

Abstract

Let G G be an abelian collineation group of order n 2 n^2 of a projective plane of order n n . We show that n n must be a prime power, and that the p p -rank of G G is at least b + 1 b+1 if n = p b n=p^b for an odd prime p p .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2002-130-05/S0002-9939-01-06388-2/S0002-9939-01-06388-2.pdf

Reference7 articles.

1. On Frobeniusean algebras. I;Nakayama, Tadasi;Ann. of Math. (2),1939

2. Planes of order 𝑛 with collineation groups of order 𝑛²;Dembowski, Peter;Math. Z.,1968

3. Quasiregular collineation groups of finite projective planes;Dembowski, Peter;Math. Z.,1967

4. On the values assumed by polynomials;Levi, Howard;Bull. Amer. Math. Soc.,1939

5. Relative difference sets and quasiregular collineation groups;Ganley, Michael J.;J. Combinatorial Theory Ser. A,1975

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