Publication: Which Moufang Loops Are Associative
No Thumbnail Available
Date
1997-06
Authors
Rajah, Andrew
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
A loop is a Moufang loop if it fulfills the identity xy. zx = (x- yz)x. Nonassociative (i.e., non-group) Moufang loops of order 24, 34 and p5(p is a prime greater than 3) are known to exist. It has also been proven that all Moufang loops of order 2a (a s 3), 3fJ (P s 3) and pY (y s 4) are associative. The aim of our research is to study the following problem: "Given a positive integer m, are all Moufang loops of order m associative?" Since O. Chein has studied the problem extensively for even values of m, we Limit our research to odd values of m in Chapter 2 and Chapter 3. Writing m as the product of powers of distinct odd primes, we answer the question above affirmatively for the following values of m: (i) pq2(p<q); (.. ) 2 2 2 11 PI P2 ···Pn; (iii) p4qI qn(3<p<q;); (iv) p3q