A class of Bol loops with a subgroup of index two
| 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 | Let $G$ be a finite group and $C_2$ the cyclic group of order 2. Consider the 8 multiplicative operations $(x,y)\mapsto (x^iy^j)^k$, where $i$, $j$, $k\in\{-1, 1\}$. Define a new multiplication on $G\times C_2$ by assigning one of the above 8 multiplications to each quarter $(G\times\{i\})\times(G\times\{j\})$, for $i$, $j\in C_2$. We describe all situations in which the resulting quasigroup is a Bol loop. This paper also corrects an error in P. Vojtěchovský: On the uniqueness of loops $M(G,2)$. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/0701709 | |
| dc.identifier | http://arxiv.org/abs/math/0701709 | |
| dc.identifier | proceedings of Loops '03, Prague, published in Comment. Math. Univ. Carolin. 45, no. 2 (2004), 371-381 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122609 | |
| dc.subject | Group Theory | |
| dc.subject | 20N05 | |
| dc.title | A class of Bol loops with a subgroup of index two | |
| dc.type | text |