Група автоморфiзмiв варiанта решiтки розбиттiв скiнченної множини

O G Ganyushkin,O O Desiateryk

doi:10.17721/1812-5409.2020/3.13

Abstract

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.

Highlights

For any semigroup S with the fixed element a ∈ S and arbitrary elements x, y ∈ S we set x∗ay = xay
We study variants of lattices which are considered as semigroups with respect to the operation ∧
A transformation φ : L → L is an automorphism of a lattice L as a

Summary

Bulletin of Taras Shevchenko National University of Kyiv

У роботi вивчаються групи автоморфiзмiв варiантiв напiвгрупи решiтки розбиттiв скiнченної множини. Що група автоморфiзмiв варiанта напiвгрупи розбиттiв скiнченної множини iзоморфна узагальненому вiнцевому добутку, в якому перший множник є прямим добутком вiнцевих добуткiв, якi задаються блоками, рiзних потужностей, розбиття, яке породжує варiант, а другий деякому набору симетричних груп. 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.

Introduction

Let the partition ρ be of the next form

Automorphisms of variants of the semigroup Partn

Список використаних джерел the rule