Admissible orders of Jordan loops

Details Admissible orders of Jordan loops Admissible orders of Jordan loops

2007-05-23

arxiv.org/abs/0705.3445v2

J. Combinatorial Designs 17 (2009), no. 2, 103-118

Mathematics

Group Theory

15 pages. V2: final version with small changes suggested by referee, to appear in J. Combinatorial Design

Scientific paper

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.

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