Admissible Orders of Jordan Loops | Zendy

Kinyon Michael K. | Zendy; Pula Kyle | Zendy; Vojtěchovský Petr | Zendy

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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

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