  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 $m$-almost quasigroup ($m$-AQ) quandle
which is a generalization of a quasigroup quandle and study annihilation of
torsion in its rack and quandle homology groups.
