Which Moufang Loops Are Associative
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 associa...
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| Format: | Thesis |
| Language: | English |
| Published: |
1997
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| Subjects: | |
| Online Access: | http://eprints.usm.my/63814/ |
| Abstract | Abstract here |
| Summary: | 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 |
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