The structure of extra loops
| dc.creator | Kinyon, Michael K. | |
| dc.creator | Kunen, Kenneth | |
| dc.date | 2004-04-14 | |
| dc.date | 2004-07-08 | |
| dc.date.accessioned | 2026-07-07T05:07:26Z | |
| dc.date.available | 2026-07-07T05:07:26Z | |
| dc.description | The Sylow theorems hold for finite extra loops, as does P. Hall's theorem for finite solvable extra loops. Every finite nonassociative extra loop $Q$ has a nontrivial center, $Z(Q)$. Furthermore, $Q/Z(Q)$ is a group whenever $|Q| < 512$. Loop extensions are used to construct an infinite nonassociative extra loop with a trivial center and a nonassociative extra loop $Q$ of order 512 such that $Q/Z(Q)$ is nonassociative. There are exactly 16 nonassociative extra loops of order $16p$ for each odd prime $p$. | |
| dc.description | 18 pages, AMS-LaTeX; v.3: minor corrections suggested by referee | |
| dc.identifier | https://arxiv.org/abs/math/0404266 | |
| dc.identifier | http://arxiv.org/abs/math/0404266 | |
| dc.identifier | Quasigroups and Related Systems 12 (2004), 39-60 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70860 | |
| dc.subject | Group Theory | |
| dc.subject | 20N05 | |
| dc.title | The structure of extra loops | |
| dc.type | text |