Mappings of Galois planes preserving the unit Euclidean distance (Q1067610)
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scientific article; zbMATH DE number 3929836
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Mappings of Galois planes preserving the unit Euclidean distance |
scientific article; zbMATH DE number 3929836 |
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Mappings of Galois planes preserving the unit Euclidean distance (English)
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1985
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The following theorem is proved: Theorem: Let \(K=GF(p^ m)\), \(p\neq 2,3\) a prime, and \(\sigma: K^ 2\to K^ 2\) be a map preserving the unit Euclidean distance. Then \(\sigma\) is an automorphism of the vector space \(K^ 2\) over GF(p), composed with a translation of \(K^ 2\). Moreover if \(m=1\), \(\sigma\) is an isometry.
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Galois plane
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unit Euclidean distance
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isometry
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