On subnormal subgroups of skew fields
type: Item
instance of: scholarly article
title: On subnormal subgroups of skew fields
zbMATH Open document ID: 0645.16013
DOI: 10.1016/0021-8693(88)90295-5
published in: Journal of Algebra
publication date: 1988-01-01T00:00:00Z
review text: Let D be a skew field with center Z, F be a free group with two generators \(x_ 1\), \(x_ 2\), \(D\{x_ 1,x_ 2\}=D*_ ZZF\) be the free product over Z, where ZF is the group ring. The author calls \(P(x_ 1,x_ 2)\in D\{x_ 1,x_ 2\}\setminus D\) a generalized Laurent polynomial. It is proved that if Z is infinite and \([D:Z]=\infty\) then any subnormal subgroup of \(D^*\) which satisfies a Laurent generalized polynomial identity is central.
Mathematics Subject Classification ID: 16Kxx
Mathematics Subject Classification ID: 16U60
Mathematics Subject Classification ID: 16Rxx
zbMATH DE Number: 4051827
zbMATH Keywords: skew field
zbMATH Keywords: free product
zbMATH Keywords: group ring
zbMATH Keywords: subnormal subgroup
zbMATH Keywords: Laurent generalized polynomial identity
author: Leonid Makar-Limanov
reviewed by: Leonid A. Bokut'
MaRDI profile type: Publication
full work available at URL: 0021-8693(88)90295-5
OpenAlex ID: W2045753673
cites work: A generalization of a theorem on linear differential equations
cites work: Generalized Polynomial Identities and Pivotal Monomials
cites work: The Theory of Simple Rings
cites work: The diamond lemma for ring theory
cites work: Are there free groups in division rings?
cites work: Prime rings satisfying a generalized polynomial identity
cites work: On the Multiplicative Group of a Division Ring
cites work: A Generalization of the Cartan-Brauer-Hua Theorem
description: scientific article; zbMATH DE number 4051827