Bol loops and Bruck loops of order pq
Right Bol loops are loops satisfying the identity ((zx)y)x=z((xy)x), and right Bruck loops are right Bol loops satisfying the identity (xy)−1=x−1y−1. Let p and q be odd primes such that p>q. Advancing the research program of Niederreiter and Robinson from 1981, we classify right Bol loops of orde...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2017
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| Sorozat: | JOURNAL OF ALGEBRA
473 |
| Tárgyszavak: | |
| doi: | 10.1016/j.jalgebra.2016.11.023 |
| mtmt: | 3181568 |
| Online Access: | http://publicatio.bibl.u-szeged.hu/29125 |
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| 024 | 7 | |a 3181568 |2 mtmt | |
| 040 | |a SZTE Publicatio Repozitórium |b hun | ||
| 041 | |a Angol | ||
| 100 | 1 | |a Kinyon Michael K. | |
| 245 | 1 | 0 | |a Bol loops and Bruck loops of order pq |h [elektronikus dokumentum] / |c Kinyon Michael K. |
| 260 | |c 2017 | ||
| 300 | |a 481-512 | ||
| 490 | 0 | |a JOURNAL OF ALGEBRA |v 473 | |
| 520 | 3 | |a Right Bol loops are loops satisfying the identity ((zx)y)x=z((xy)x), and right Bruck loops are right Bol loops satisfying the identity (xy)−1=x−1y−1. Let p and q be odd primes such that p>q. Advancing the research program of Niederreiter and Robinson from 1981, we classify right Bol loops of order pq. When q does not divide p2−1, the only right Bol loop of order pq is the cyclic group of order pq. When q divides p2−1, there are precisely (p−q+4)/2 right Bol loops of order pq up to isomorphism, including a unique nonassociative right Bruck loop Bp,q of order pq. Let Q be a nonassociative right Bol loop of order pq. We prove that the right nucleus of Q is trivial, the left nucleus of Q is normal and is equal to the unique subloop of order p in Q, and the right multiplication group of Q has order p2q or p3q. When Q=Bp,q, the right multiplication group of Q is isomorphic to the semidirect product of Zp×Zp with Zq. Finally, we offer computational results as to the number of right Bol loops of order pq up to isotopy. © 2016 Elsevier Inc. | |
| 650 | 4 | |a Matematika | |
| 700 | 0 | 1 | |a Nagy Gábor Péter |e aut |
| 700 | 0 | 1 | |a Vojtěchovský Petr |e aut |
| 856 | 4 | 0 | |u http://publicatio.bibl.u-szeged.hu/29125/1/KinyonNagyVojtechovskyBolloopsandBruckloopsoforderpq2017.pdf |z Dokumentum-elérés |