Automorphism groups of some variants of lattices

Authors

  • O.G. Ganyushkin Taras Shevchenko National University of Kyiv, 64/13 Volodymyrska str., 01601, Kyiv, Ukraine
  • O.O. Desiateryk Taras Shevchenko National University of Kyiv, 64/13 Volodymyrska str., 01601, Kyiv, Ukraine https://orcid.org/0000-0002-7591-3846
https://doi.org/10.15330/cmp.13.1.142-148

Keywords:

lattice, variant, sandwich semigroup, automorphism group, power set, subspaces lattice, generating set
Published online: 2021-06-20

Abstract

In this paper we consider variants of the power set and the lattice of subspaces and study automorphism groups of these variants. We obtain irreducible generating sets for variants of subsets of a finite set lattice and subspaces of a finite vector space lattice.

We prove that automorphism group of the variant of subsets of a finite set lattice is a wreath product of two symmetric permutation groups such as first of this groups acts on subsets. The automorphism group of the variant of the subspace of a finite vector space lattice is a natural generalization of the wreath product. The first multiplier of this generalized wreath product is the automorphism group of subspaces lattice and the second is defined by the certain set of symmetric groups.

Article metrics
How to Cite
(1)
Ganyushkin, O.; Desiateryk, O. Automorphism Groups of Some Variants of Lattices. Carpathian Math. Publ. 2021, 13, 142-148.