On planes of prime order with translations and homologies (Q1117457)
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scientific article; zbMATH DE number 4092231
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On planes of prime order with translations and homologies |
scientific article; zbMATH DE number 4092231 |
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On planes of prime order with translations and homologies (English)
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1989
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It has long been conjectured that any affine plane A of prime order p must be Desarguesian. In this paper it is shown that if A admits translations and also a homology with axis \(\ell_{\infty}\) of order \(1/2 (p-1)\), then A is Desarguesian indeed. The proof is based on a result, also proved here, on the orthomorphism graph of \({\mathbb{Z}}/(p)\).
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(p-2)-clique
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affine plane of prime order
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Desarguesian
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translations
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homology
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orthomorphism graph of \({\mathbb{Z}}/(p)\)
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