Admissible orders of Jordan loops

Abstract

A commutative loop is Jordan if it satisfies the identity $x^2(yx)=(x^{2}y)x$. Using an amalgam construction and its generalizations, we prove that a nonassociative Jordan loop of order $n$ exists if and only if $n\ge 6$ and $n\ne 9$. 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

Cited by in corpus (1)

• Powers of Elements in Jordan Loops