On the representation of lattices by subgroup lattices
type: Item
instance of: scholarly article
title: On the representation of lattices by subgroup lattices
zbMATH Open document ID: 0902.06007
DOI: 10.1007/PL00000330
published in: Algebra Universalis
publication date: 1998-11-23T00:00:00Z
review text: \textit{P. M. Whitman} [Bull. Am. Math. Soc. 52, 507-522 (1946; Zbl 0060.06505)] proved that every lattice can be embedded in the subgroup lattice of a suitable group. In this paper the author studies the problem of embedding in lattices of subgroups of relatively free (i.e. free in a variety) groups. He proves that any lattice satisfying Whitman's condition can be embedded in the subgroup lattice of a free group of an arbitrary non-soluble group variety. Some interesting corollaries are examined.
Mathematics Subject Classification ID: 06B15
Mathematics Subject Classification ID: 20E15
zbMATH DE Number: 1226192
zbMATH Keywords: lattice
zbMATH Keywords: embedding
zbMATH Keywords: subgroup lattice
author: Vladimir B. Repnitskiǐ
reviewed by: Radomír Halaš
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1226192