Loops of order \(p^ n+1\) with transitive automorphism groups (Q1362612)
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scientific article; zbMATH DE number 1044215
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Loops of order \(p^ n+1\) with transitive automorphism groups |
scientific article; zbMATH DE number 1044215 |
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Loops of order \(p^ n+1\) with transitive automorphism groups (English)
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25 January 1998
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The author proves that isotopic loops of order \(p^n+1\), \(p\) a prime, which have transitive automorphism groups, are in fact isomorphic. The proof uses the Sylow theorems to obtain an isomorphism from an arbitrary isotopism. The result implies a corollary: If \(N_1\) and \(N_2\) are neofields of order \(p^n+1\), then the additive loops of \(N_1\) and \(N_2\) are isotopic if and only if they are isomorphic.
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isotopic loops
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transitive automorphism groups
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Sylow theorems
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isomorphisms
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isotopisms
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neofields
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additive loops
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