Dualities of groups
type: Item
instance of: scholarly article
title: Dualities of groups
zbMATH Open document ID: 0871.20022
DOI: 10.1007/BF01758982
author: G. Zacher
author: Stewart Stonehewer
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1997-10-05T00:00:00Z
review text: Let \(G\) and \(\overline G\) be groups. A duality from \(G\) to \(\overline G\) is a bijection \(\delta\) from the set of all subgroups of \(G\) to the set of all subgroups of \(\overline G\) such that \(\delta\) and \(\delta^{-1}\) reverse inclusions. The Tarski groups are the first non-soluble examples of self-dual groups. The aim of this paper is to study the structure of groups admitting dualities. In particular modular groups with duals and locally graded groups admitting an autoduality satisfying some further requirements are considered.
Mathematics Subject Classification ID: 20E15
zbMATH DE Number: 1000256
zbMATH Keywords: subgroup lattices
zbMATH Keywords: self-dual groups
zbMATH Keywords: groups admitting dualities
zbMATH Keywords: modular groups
zbMATH Keywords: locally graded groups
zbMATH Keywords: autoduality
reviewed by: Silvana Franciosi
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01758982
OpenAlex ID: W1969000339
description: scientific article; zbMATH DE number 1000256