On the uniqueness of loops M(G,2)
| 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 $i$, $j\in C_2$. When $G$ is nonabelian then exactly four assignments yield Moufang loops that are not associative; all (anti)isomorphic, known as loops $M(G,2)$. | |
| dc.description | 5 pages, revised, the published version contains an error, see "A class of Bol loops with a subgroup of index two" by P.V. for more details | |
| dc.identifier | https://arxiv.org/abs/math/0701705 | |
| dc.identifier | http://arxiv.org/abs/math/0701705 | |
| dc.identifier | Comment. Math. Univ. Carolin., 44 (2003), no. 4, 629-635 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122605 | |
| dc.subject | Group Theory | |
| dc.subject | 20N05 | |
| dc.title | On the uniqueness of loops M(G,2) | |
| dc.type | text |