Subquandles of affine quandles
Group Theory
2018-06-06 v2
Abstract
A quandle will be called quasi-affine, if it embeds into an affine quandle. Our main result is a characterization of quasi-affine quandles, by group-theoretic properties of their displacement group, by a universal algebraic condition coming from the commutator theory, and by an explicit construction over abelian groups. As a consequence, we obtain efficient algorithms for recognizing affine and quasi-affine quandles, and we enumerate small quasi-affine quandles. We also prove that the "abelian implies quasi-affine" problem of universal algebra has affirmative answer for the class of quandles.
Keywords
Cite
@article{arxiv.1708.02362,
title = {Subquandles of affine quandles},
author = {Přemysl Jedlička and Agata Pilitowska and David Stanovský and Anna Zamojska-Dzienio},
journal= {arXiv preprint arXiv:1708.02362},
year = {2018}
}