Some structure theorems for \(\omega\)-stable groups
type: Item
instance of: scholarly article
title: Some structure theorems for \(\omega\)-stable groups
zbMATH Open document ID: 0644.03018
author: Katsumi Tanaka
published in: Proceedings of the Japan Academy. Series A
publication date: 1987-01-01T00:00:00Z
review text: The author proves here that every locally supersolvable group of finite Morley rank is nilpotent-by-finite, and hence hypercyclic. This is motivated by the analogous result of \textit{C. A. Higgins} [J. Lond. Math. Soc., II. Ser. 20, 53-59 (1979; Zbl 0413.20028)] about CZ-groups: both CZ-groups and groups of finite Morley rank are abstractions of algebraic groups and so are reasonably expected to share the same structure theorems, and in fact it is an open question whether groups of finite Morley rank are CZ-groups, i.e. carry a \(T_ 1\) topology with the DCC on closed sets, and such that the following maps: \(x\to ax\), xa, \(x^{-1}\), \(xax^{-1}\), are continuous.
Mathematics Subject Classification ID: 03C60
Mathematics Subject Classification ID: 03C45
Mathematics Subject Classification ID: 20F16
zbMATH DE Number: 4049625
zbMATH Keywords: locally supersolvable group
zbMATH Keywords: finite Morley rank
zbMATH Keywords: nilpotent-by-finite
zbMATH Keywords: hypercyclic
zbMATH Keywords: CZ-groups
reviewed by: Chantal Berline
MaRDI profile type: Publication
full work available at URL: pjaa.63.254
OpenAlex ID: W2077928319
cites work: Q4109668
cites work: Superstable groups; a partial answer to conjectures of Cherlin and Zil'ber
cites work: Groups of small Morley rank
cites work: Some Structure Theorems for CZ -Groups
cites work: Q3255437
cites work: Q5654235
cites work: Some local properties of \(\omega\)-stable groups
cites work: Q5676405
cites work: Some model theory of simple algebraic groups over algebraically closed fields
DOI: 10.3792/PJAA.63.254
description: scientific article; zbMATH DE number 4049625