On the simplicity of the multiplicative group of an existentially closed skew field
type: Item
instance of: scholarly article
title: On the simplicity of the multiplicative group of an existentially closed skew field
zbMATH Open document ID: 0942.16033
DOI: 10.1007/BF03322025
author: Otto H. Kegel
published in: Results in Mathematics
publication date: 2000-06-13T00:00:00Z
review text: Let \(Z\) be a commutative field and \(C\) the class of skew-fields with center \(Z\). It is shown that the group \(G=E^*/Z^*\) is simple. It is also proved, along with several other related results, that if \(Z\) is algebraically closed, then \(G\) is torsion-free and its elements other than the unit form a single conjugacy class. The proofs depend on a theorem due to P. M. Cohn, and the paper is written in honour of his 75-th Birthday. In the second equation of \((1,d)\), \(x\) should be replaced by \(t\).
Mathematics Subject Classification ID: 16U60
Mathematics Subject Classification ID: 16K40
Mathematics Subject Classification ID: 12E15
Mathematics Subject Classification ID: 20E32
zbMATH DE Number: 1294485
zbMATH Keywords: existentially closed skew fields
zbMATH Keywords: simple groups
zbMATH Keywords: groups of units
zbMATH Keywords: central factors
reviewed by: Richard M. Cohn
MaRDI profile type: Publication
cites work: On the free product of associative rings. II: The case of (skew) fields
cites work: The Embedding of Firs in Skew Fields
cites work: Q4848757
cites work: Embedding Theorems for Groups
cites work: Forcing, arithmetic, division rings
description: scientific article; zbMATH DE number 1294485