The structure of extra loops

dc.creatorKinyon, Michael K.
dc.creatorKunen, Kenneth
dc.date2004-04-14
dc.date2004-07-08
dc.date.accessioned2026-07-07T05:07:26Z
dc.date.available2026-07-07T05:07:26Z
dc.descriptionThe 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.description18 pages, AMS-LaTeX; v.3: minor corrections suggested by referee
dc.identifierhttps://arxiv.org/abs/math/0404266
dc.identifierhttp://arxiv.org/abs/math/0404266
dc.identifierQuasigroups and Related Systems 12 (2004), 39-60
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70860
dc.subjectGroup Theory
dc.subject20N05
dc.titleThe structure of extra loops
dc.typetext

Files

Collections