Open AccessAutomorphism groups of some variants of lattices
Author(s) -
Olexandr Ganyushkin,
Oleksandra Desiateryk
Publication year - 2021
Publication title -
karpatsʹkì matematičnì publìkacìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.63
H-Index - 4
eISSN - 2313-0210
pISSN - 2075-9827
DOI - 10.15330/cmp.13.1.142-148
Subject(s) - mathematics , wreath product , linear subspace , automorphism , combinatorics , vector space , lattice (music) , inner automorphism , permutation group , subspace topology , automorphism group , direct product , symmetric group , discrete mathematics , pure mathematics , permutation (music) , product (mathematics) , mathematical analysis , physics , geometry , acoustics
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.