2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137403In 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.8 pages, in RussianMathematical Physics55M99text