Abelian quandles and quandles with abelian structure group

Sets with a self-distributive operation (in the sense of ( ◃ b ) c = ), in particular quandles, appear knot and braid theories, Hopf algebra classification, study Yang–Baxter equation, other areas. An important invariant quandles is their structure group. The group finite quandle known to be either “boring” (free abelian), or “interesting” (non-abelian torsion). In this paper we explicitly describe all abelian To achieve this, show that such are (i.e., satisfy ); present any as central extension free by an explicit ; determine when latter trivial. second part paper, relate its 2nd homology H 2 . We use prove torsion-free, but general may exhibit torsion. Torsion for constructing invariants pointed algebras.