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Nilpotence of finite Moufang 2-loops

โœ 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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๐Ÿ“œ SIMILAR VOLUMES


Nilpotent Moufang Unit Loops
โœ Edgar G. Goodaire; Cรฉsar Polcino Milies ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 193 KB
Generators of Nonassociative Simple Mouf
โœ Petr Vojtฤ›chovskรฝ ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 70 KB

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.

Moufang Loops of Even Order
โœ L. Fook; T.P. Eng ๐Ÿ“‚ Article ๐Ÿ“… 1994 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 185 KB
On Moufang Loops of Odd Order pq2
โœ F. Leong; A. Rajah ๐Ÿ“‚ Article ๐Ÿ“… 1995 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 194 KB
Moufang Loops of Odd Order pq3
โœ Andrew Rajah ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 187 KB

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 . แฎŠ 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

Moufang Loops of Odd Orderp12p22ยทยทยทpm2
โœ Fook Leong; Andrew Rajah ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 126 KB

It has been proven in F. Leong and A. Rajah, J. Algebra, 176 1995 , 265แސ270 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 โฃ F 2.