  We prove that if Q is a finite quasigroup quandle, then |Q| annihilates the
torsion of its homology. It is a classical result in reduced homology of finite
groups that the order of a group annihilates its homology. From the very
beginning of the rack homology (between 1990 and 1995) the analogous result was
suspected. The first general results in this direction were obtained
independently about 2001 by R.A.Litherland and S.Nelson, and P.Etingof and
M.Grana. In Litherland-Nelson paper it is proven that if (Q;*) is a finite
homogeneous rack (this includes quasigroup racks) then the torsion of homology
is annihilated by |Q|^n. In Etingof-Grana paper it is proven that if (X;A) is a
finite rack and N=|G^0_Q| is the order of a group of inner automorphisms of Q,
then only primes which can appear in the torsion of homology are those dividing
N (the case of connected Alexander quandles was proven before by T.Mochizuki).
The result of Litherland-Nelson is generalized by Niebrzydowski and Przytycki
and in particular, they prove that the torsion part of the homology of the
dihedral quandle R_3 is annihilated by 3. In Niebrzydowski-Przytycki paper it
is conjectured that for a finite quasigroup quandle, torsion of its homology is
annihilated by the order of the quandle. The conjecture is proved by T.Nosaka
for finite Alexander quasigroup quandles. In this paper we prove the conjecture
in full generality. For this version, we rewrote the Section 3 totally and
introduced the concept of the precubic homotopy. In Section 2, the main
addition is Corollary 2.2 which summarizes identities observed in the proof of
the main theorem as we use it later in Section 3.
