Quandles with orbit series conditions
Group Theory
2020-08-20 v3
Abstract
We introduce the notion of an orbit series in a quandle. Using this notion we define four families of quandles based on finiteness conditions on their orbit series. Intuitively, the classes tOS and tOSn correspond to finitary compositions of trivial quandles while the classes OS and OSn correspond to finitary compositions of connected quandles. We study properties of these four families of quandles and explore their relationships with several previously studied families of quandles: reductive, n-reductive, locally reductive, n-locally reductive, and solvable quandles.
Cite
@article{arxiv.2004.10227,
title = {Quandles with orbit series conditions},
author = {Marco Bonatto and Alissa S. Crans and Timur Nasybullov and Glen T. Whitney},
journal= {arXiv preprint arXiv:2004.10227},
year = {2020}
}
Comments
Additional clarification of some proofs, typos fixed, and Question 5.7 added