C-loops: extensions and constructions
| dc.creator | Kinyon, Michael K. | |
| dc.creator | Phillips, J. D. | |
| dc.creator | Vojtěchovský, Petr | |
| dc.date | 2004-12-19 | |
| dc.date.accessioned | 2026-07-07T08:54:24Z | |
| dc.date.available | 2026-07-07T08:54:24Z | |
| dc.description | C-loops are loops satisfying the identity $x(y\cdot yz) = (xy\cdot y)z$. We develop the theory of extensions of C-loops, and characterize all nuclear extensions provided the nucleus is an abelian group. C-loops with central squares have very transparent extensions; they can be built from small blocks arising from the underlying Steiner triple system. Using these extensions, we decide for which abelian groups $K$ and Steiner loops $Q$ there is a nonflexible C-loop $C$ with center $K$ such that $C/K$ is isomorphic to $Q$. We discuss possible orders of associators in C-loops. Finally, we show that the loops of signed basis elements in the standard real Cayley-Dickson algebras are C-loops. | |
| dc.description | 17 pages, amsart | |
| dc.identifier | https://arxiv.org/abs/math/0412390 | |
| dc.identifier | http://arxiv.org/abs/math/0412390 | |
| dc.identifier | J. Algebra and its Applications 6 (2007), 1-20 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/145918 | |
| dc.subject | Group Theory | |
| dc.subject | 20N05 | |
| dc.title | C-loops: extensions and constructions | |
| dc.type | text |