Nilpotence of finite Moufang 2-loops
โ Scribed by G Glauberman; C.R.B Wright
- Publisher
- Elsevier Science
- Year
- 1968
- Tongue
- English
- Weight
- 150 KB
- Volume
- 8
- Category
- Article
- ISSN
- 0021-8693
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๐ SIMILAR VOLUMES
We present an elementary proof that the nonassociative simple Moufang loops over finite prime fields are generated by three elements. In the last section, we conclude that integral Cayley numbers of unit norm are generated multiplicatively by three elements.
In this paper, we prove the existence of nonassociative Moufang loops of order pq 3 ลฝ . for every pair of odd primes, p and q with q ' 1 mod p . แฎ 2001 Academic Press 11 that all Moufang loops of odd order pq with pq are groups, but w x later withdrew the result 12 after a flaw was found by Leong a
It has been proven in F. Leong and A. Rajah, J. Algebra, 176 1995 , 265แ270 that all Moufang loops of odd order pq 2 are groups for distinct primes p and q. In this paper, we generalize this result to Moufang loops of odd order p where p are distinct primes and โฃ F 2.