An identity for subgroup lattices of Abelian groups
type: Item
instance of: scholarly article
title: An identity for subgroup lattices of Abelian groups
zbMATH Open document ID: 0820.06003
DOI: 10.1007/BF01190930
published in: Algebra Universalis
publication date: 1995-07-04T00:00:00Z
review text: This well-written, important paper contains the solution of the following long-standing problem: Does there exist a lattice-identity holding in the subgroup lattice of every Abelian group which fails in the lattice of normal subgroups of some finite group? The Theorem of this paper presents such an identity. It fails for a two- group. The paper mentions an unpublished result of Emil Kiss and the first author ``on the road'' leading to this theorem. The authors give only a rough sketch on the projective geometric background of the theorem. Those who want to understand the geometric part should read the longer version: ``Congruence varieties of groups and Abelian groups'', written by the same authors, which will appear in: Lattice Theory and its Application (edited by K. A. Baker and R. Wille), 163-183 (Heldermann Verlag, 1995).
Mathematics Subject Classification ID: 06B15
Mathematics Subject Classification ID: 06C05
zbMATH DE Number: 750788
zbMATH Keywords: Arguesian identities
zbMATH Keywords: projective geometry
zbMATH Keywords: lattice-identity
zbMATH Keywords: subgroup lattice
zbMATH Keywords: Abelian group
zbMATH Keywords: normal subgroups
author: Péter P. Pálfy
author: Csaba Szabó
reviewed by: Ervin Fried
MaRDI profile type: Publication
cites work: Proof theory for linear lattices
cites work: Finite fixed point algebras are subdiagonalisable
cites work: On the representation of lattices
full work available at URL: https://doi.org/10.1007/bf01190930
OpenAlex ID: W103537192
description: scientific article; zbMATH DE number 750788