Annihilation of torsion in homology of finite m-AQ quandles

Abstract

It is a classical result in reduced homology of finite groups that the order of a group annihilates its homology. Similarly, we have proved that the torsion subgroup of rack and quandle homology of a finite quasigroup quandle is annihilated by its order. However, it does not hold for connected quandles in general. In this paper, we define an [Formula: see text]-almost quasigroup ([Formula: see text]-AQ) quandle which is a generalization of a quasigroup quandle and study annihilation of torsion in its rack and quandle homology groups.