Automorphism group of the variant of the lattice of partitions of a finite set

Ganyushkin, O. G., Desiateryk, O. O. (2020). Automorphism group of the variant of the lattice of partitions of a finite set. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics(3), 115–119. https://doi.org/10.17721/1812-5409.2020/3.13

In this paper we consider variants of the lattice of partitions of a finite set and study automorphism groups of this variants. We obtain irreducible generating sets for of the lattice of partitions of a finite set.We prove that the automorphism group of the variant of the lattice of partitions of a finite set is a natural generalization of the wreath product. The first multiplier of this generalized wreath product is the direct product of the wreaths products, such that depends on the type of the variant generating partition and the second is defined by the certain set of symmetric groups.Key words: semigroup, variant, lattice, automorphism group.Pages of the article in the issue: 115 - 119Language of the article: English