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The isomorphism problem for abelian projective planes

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Abstract

We settle the isomorphism problem for finite cyclic projective planes by proving the following analogue of the Bays–Lambossy theorem: two cyclic projective planes of order n are isomorphic if and only if they are multiplier equivalent, that is, if and only if the associated difference sets in \({\mathbb{Z}_{n^2+n+1}}\) are equivalent. In fact, we establish a more general result for abelian groups, where multipliers are replaced by group automorphisms.

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  1. Lehrstuhl für Diskrete Mathematik, Optimierung und Operations Research, Universität Augsburg, 86135, Augsburg, Germany

    Dieter Jungnickel

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  1. Dieter Jungnickel
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Correspondence to Dieter Jungnickel.

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Jungnickel, D. The isomorphism problem for abelian projective planes. AAECC 19, 195–200 (2008). https://doi.org/10.1007/s00200-008-0070-4

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  • DOI: https://doi.org/10.1007/s00200-008-0070-4

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