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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Proof of the prime power conjecture for projective planes of order $n$ with abelian collineation groups of order $n^2$


Authors: Aart Blokhuis, Dieter Jungnickel and Bernhard Schmidt
Journal: Proc. Amer. Math. Soc. 130 (2002), 1473-1476
MSC (2000): Primary 51E15; Secondary 05B10
Published electronically: December 20, 2001
MathSciNet review: 1879972
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Abstract: Let $G$ be an abelian collineation group of order $n^2$ of a projective plane of order $n$. We show that $n$ must be a prime power, and that the $p$-rank of $G$ is at least $b+1$ if $n=p^b$ for an odd prime $p$.


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Additional Information

Aart Blokhuis
Affiliation: Department of Mathematics and Computing Science, Eindhoven University of Technology, Den Dolech 2, P.O. Box 513, 5600 MB Eindhoven, Netherlands
Email: aart@win.tue.nl

Dieter Jungnickel
Affiliation: Institut für Mathematik, Universität Augsburg, Universitätsstraße 14, 86135 Augsburg, Germany
Email: jungnickel@math.uni-augsburg.de

Bernhard Schmidt
Affiliation: Institut für Mathematik, Universität Augsburg, Universitätsstraße 14, 86135 Augsburg, Germany
Email: schmidt@math.uni-augsburg.de

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06388-2
PII: S 0002-9939(01)06388-2
Received by editor(s): November 17, 2000
Published electronically: December 20, 2001
Communicated by: Stephen D. Smith
Article copyright: © Copyright 2001 American Mathematical Society