\(\overline R\)-groups
type: Item
instance of: scholarly article
title: \(\overline R\)-groups
zbMATH Open document ID: 0931.20024
author: Temple H. Fay
author: G. L. Walls
published in: Journal of Algebra
publication date: 2000-02-28T00:00:00Z
review text: The authors introduce a new class of torsionfree groups, called \(\overline R\)-groups, in which the normalizer and centralizer of the isolator of each cyclic subgroup coincide. These groups share many interesting properties with the class of all \(R\)-groups, groups having unique roots. For example, they show that the class of \(\overline R\)-groups is closed under products, subgroups, restricted wreath products, free products, and certain free products with amalgamation. The authors also introduce closure operators and investigate the concomitant categorically compact classes associated with these operators. These new compact classes are closed under finite products and homomorphic images and their characterization generally involves the existence of roots of all orders for elements of the hypercenter.
Mathematics Subject Classification ID: 20E34
Mathematics Subject Classification ID: 20E22
Mathematics Subject Classification ID: 20J15
zbMATH DE Number: 1271658
zbMATH Keywords: torsionfree groups
zbMATH Keywords: normalizers
zbMATH Keywords: centralizers
zbMATH Keywords: isolators
zbMATH Keywords: cyclic subgroups
zbMATH Keywords: groups having unique roots
zbMATH Keywords: wreath products
zbMATH Keywords: free products
zbMATH Keywords: free products with amalgamation
zbMATH Keywords: closure operators
zbMATH Keywords: categorically compact classes
zbMATH Keywords: existence of roots
zbMATH Keywords: hypercenters
reviewed by: Alexander Ivanovich Budkin
MaRDI profile type: Publication
full work available at URL: jabr.1998.7611
OpenAlex ID: W4210781653
cites work: Some aspects of groups with unique roots
cites work: Q3720766
cites work: Closure operators. I
cites work: Q4859897
cites work: Regular and normal closure operators and categorical compactness for groups
cites work: COMPLETIONS AND CATEGORICAL COMPACTNESS FOR NILPOTENT GROUPS
cites work: A characterization of categorically compact locally nilpotent groups
cites work: Categorically compact locally nilpotent groups:a corrigendum
cites work: Categorically compact locally nilpotent groups
cites work: Compact nilpotent groups
cites work: Factorizations, denseness, separation, and relatively compact objects
cites work: Q3270631
cites work: Compact Hausdorff objects
cites work: On some criteria of locally nilpotent groups
cites work: Q4102451
cites work: Q5331572
DOI: 10.1006/JABR.1998.7611
description: scientific article; zbMATH DE number 1271658