A G-loop is a loop which is isomorphic to all its loop isotopes. We apply some theorems about permutation groups to get information about G-loops. In particular, we study G-loops of order pq, where p < q are primes and p q -1 . In the case p = 3, the only G-loop of order 3q is the group of order 3q.
Permutation representations of loops
โ Scribed by Jonathan D.H. Smith
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 142 KB
- Volume
- 264
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
We give a combinatorial proof of the formula giving the number of representations of an even permutation ฯ in S n as a product of an n-cycle by an (n -2)-cycle, such a number being (nฯ(ฯ ))(n -3)!, where ฯ(ฯ ) is the number of fixed points of ฯ . This proof relies on the fact that any odd permutatio
New techniques, both theoretical and practical, are presented for constructing permutation representations for computing with matrix groups defined over finite fields. The permutation representation is constructed on a conjugacy class of subgroups of prime order. We construct a base for the permutat