Algebra and topology of factor-lattices

In this paper we investigate the relation between Abelian and non-Abelian groups of parity. The Abelian groups of parity are formed as kernels of homomorphisms of parity in group $\mmathbb{Z}^{n}$ and the non-Abelian groups of parity are formed as kernels of homomorphisms of parity in group $S_{2}\wr S_{n}$. It is shown that the group of isomorphisms of the factor-lattice recieved by factorization of regular lattice with help of some Abelian group is equal to the corresponding non-Abelian group.