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Algebra and topology of factor-lattices

Igor Bayak
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Abstract

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.

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Igor Bayak. 2007-09-06. Algebra and topology of factor-lattices. https://arxiv.org/abs/math-ph/0603072

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