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Admissible Orders of Jordan Loops
Author(s) -
Kinyon Michael K.,
Pula Kyle,
Vojtěchovský Petr
Publication year - 2009
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.20186
Subject(s) - mathematics , loop (graph theory) , identity (music) , order (exchange) , simple (philosophy) , commutative property , combinatorics , construct (python library) , amalgam (chemistry) , pure mathematics , algebra over a field , computer science , physics , philosophy , finance , epistemology , electrode , quantum mechanics , acoustics , economics , programming language
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