Admissible Orders of Jordan Loops

✍ Scribed by Michael K. Kinyon; Kyle Pula; Petr Vojtěchovský

• Book ID: 102308952
• Publisher: John Wiley and Sons
• Year: 2009
• Tongue: English
• Weight: 164 KB
• Volume: 17
• Category: Article
• ISSN: 1063-8539
• DOI: 10.1002/jcd.20186

✦ Synopsis

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≧ 6 and n≠ 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. © 2008 Wiley Periodicals, Inc. J Combin Designs 17: 103–118, 2009