Some local properties of \(\omega\)-stable groups
type: Item
instance of: scholarly article
title: Some local properties of \(\omega\)-stable groups
zbMATH Open document ID: 0644.03017
DOI: 10.1007/BF01625832
author: Katsumi Tanaka
published in: Archive for Mathematical Logic
publication date: 1988-01-01T00:00:00Z
review text: The author shows that if G is a locally solvable group of finite Morley rank then G is solvable, and that if G is locally nilpotent of finite Morley rank and also connected, then G is nilpotent. It is pointed out that the semidirect product of \({\mathbb{Z}}(2^{\infty})\) and \({\mathbb{Z}}_ 2\), where the latter acts on the former by inversion shows that the connectedness assumption cannot be dropped.
Mathematics Subject Classification ID: 03C60
Mathematics Subject Classification ID: 03C45
Mathematics Subject Classification ID: 20F16
zbMATH DE Number: 4049624
zbMATH Keywords: omega-stable groups
zbMATH Keywords: solvable group
zbMATH Keywords: locally solvable group
zbMATH Keywords: finite Morley rank
zbMATH Keywords: locally nilpotent
zbMATH Keywords: connectedness
reviewed by: Anand Pillay
MaRDI profile type: Publication
cites work: Stability theory and Algebra
cites work: Q4109668
cites work: Totally categorical groups and rings
cites work: Q3208637
full work available at URL: https://doi.org/10.1007/bf01625832
OpenAlex ID: W2007349160
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description: scientific article; zbMATH DE number 4049624