2017/08/08 by Jedlička, Přemysl, Pilitowska, Agata, Stanovský, David +1
#08A05 #15A78 #20N02 #57M27 #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.1708.02362
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.