Moufang loops that share associator and three quarters of their multiplication tables
| dc.creator | Drápal, Aleš | |
| dc.creator | Vojtěchovský, Petr | |
| dc.date | 2007-01-24 | |
| dc.date.accessioned | 2026-07-07T07:42:52Z | |
| dc.date.available | 2026-07-07T07:42:52Z | |
| dc.description | Two constructions due to Drápal produce a group by modifying exactly one quarter of the Cayley table of another group. We present these constructions in a compact way, and generalize them to Moufang loops, using loop extensions. Both constructions preserve associators, the associator subloop, and the nucleus. We conjecture that two Moufang 2-loops of finite order $n$ with equivalent associator can be connected by a series of constructions similar to ours, and offer empirical evidence that this is so for $n=16$, 24, 32; the only interesting cases with $n\le 32$. We further investigate the way the constructions affect code loops and loops of type $M(G, 2)$. The paper closes with several conjectures and research questions concerning the distance of Moufang loops, classification of small Moufang loops, and generalizations of the two constructions. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/math/0701710 | |
| dc.identifier | http://arxiv.org/abs/math/0701710 | |
| dc.identifier | Rocky Mountain Journal of Mathematics 36 (2006), no. 2, 425-455 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122610 | |
| dc.subject | Group Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 20N05, 20D60, 05B15 | |
| dc.title | Moufang loops that share associator and three quarters of their multiplication tables | |
| dc.type | text |