It is shown 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 is applied to the additive loops of neofields of order p n +1. ## 1997 Aca
Loops with Transitive Automorphisms
โ Scribed by Arthur A. Drisko
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 199 KB
- Volume
- 184
- Category
- Article
- ISSN
- 0021-8693
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โฆ Synopsis
It is shown that isotopic loops with transitive automorphism groups are in fact isomorphic. A classification of loops with transitive automorphism groups is given.
ลฝ . This classification is compared to one given by Barlotti and Strambach 1983 for loops with sharply transitive automorphism groups, and examples of several of the classes are presented. The approach is entirely algebraic.
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