On some questions of the theory of partially ordered groups
type: Item
instance of: scholarly article
title: On some questions of the theory of partially ordered groups
zbMATH Open document ID: 0536.06016
DOI: 10.1007/BF01979678
author: N. Ya. Medvedev
published in: Algebra and Logic
publication date: 1983-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/187232
review text: The main results of this paper are as follows. It is proved that in each \(\ell\)-group there exists a largest convex locally nilpotent \(\ell\)- subgroup. There is constructed a linearly orderable group G having a subgroup H of finite index with a nilpotent commutant such that the commutant of G fails to be nilpotent. A partial solution of question 12 in the problem list [Notices Am. Math. Soc. 29, 327 (1982)] is given.
Mathematics Subject Classification ID: 06F15
Mathematics Subject Classification ID: 20F60
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 3851174
zbMATH Keywords: convex locally nilpotent \(\ell\)-subgroup
zbMATH Keywords: linearly orderable group
reviewed by: Ján Jakubík
MaRDI profile type: Publication
cites work: Q3904649
cites work: Q5586432
cites work: Relatively convex subgroups of orderable groups
cites work: Q3964761
cites work: Q4133686
cites work: Q3869399
cites work: Varieties of groups
OpenAlex ID: W2153311224
description: scientific article; zbMATH DE number 3851174