Admissible Orders of Jordan Loops
| Autor: | Michael Kinyon, Kyle Pula, Petr Vojtěchovský |
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| Rok vydání: | 2009 |
| Předmět: |
Discrete mathematics
Pure mathematics Jordan matrix Mathematics::Rings and Algebras 20N05 Group Theory (math.GR) Combinatorics Loop (topology) Mathematics::Group Theory Identity (mathematics) symbols.namesake Simple (abstract algebra) FOS: Mathematics symbols Discrete Mathematics and Combinatorics Order (group theory) Mathematics - Group Theory Commutative property Mathematics |
| Zdroj: | Journal of Combinatorial Designs. 17:103-118 |
| ISSN: | 1520-6610 1063-8539 |
| DOI: | 10.1002/jcd.20186 |
| Popis: | A commutative loop is Jordan if it satisfies the identity $x^2 (y x) = (x^2 y) x$. Using an amalgam construction and its generalizations, we prove that a nonassociative Jordan loop of order $n$ exists if and only if $n\geq 6$ and $n\neq 9$. We also consider whether powers of elements in Jordan loops are well-defined, and we construct an infinite family of finite simple nonassociative Jordan loops. 15 pages. V2: final version with small changes suggested by referee, to appear in J. Combinatorial Design |
| Databáze: | OpenAIRE |
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