Non-solvable groups of Morley rank 3
type: Item
instance of: scholarly article
title: Non-solvable groups of Morley rank 3
zbMATH Open document ID: 0684.03014
DOI: 10.1016/0021-8693(89)90159-2
author: Ali Nesin
published in: Journal of Algebra
publication date: 1989-01-01T00:00:00Z
review text: A bad group is a simple group of finite Morley rank with nilpotent Borel subgroups (a Borel subgroup is a maximal solvable definable connected subgroup). In the paper, it is proved that if G has Morley rank 3, then G has no involutions, each proper centralizer is connected and G is the union of the conjugates of a proper centralizer. As a corollary, one obtains the unstability of \(SO_ n({\mathbb{R}})\) for \(n\geq 3\). The proof uses the geometry of involutions developed by Bachmann. The work is a continuation of the work initiated by \textit{G. Cherlin} [Ann. Math. Logic 17, 1-28 (1979; Zbl 0427.20001)]. The same results were proved by \textit{A. Borovik} (preprint) independently. The results were generalized to minimal bad groups by \textit{L. J. Corredor} [J. Symb. Logic 54, No.3, 768- 773 (1989)] and independently by \textit{B. Poizat} and \textit{A. Borovik} [Mauvais groupes, Sib. Mat. Zhurn. (to appear)].
reviewed by: Ali Nesin
Mathematics Subject Classification ID: 03C60
zbMATH DE Number: 4120157
zbMATH Keywords: bad group
zbMATH Keywords: simple group of finite Morley rank
zbMATH Keywords: nilpotent Borel subgroups
zbMATH Keywords: involutions
MaRDI profile type: Publication
full work available at URL: 0021-8693(89)90159-2
OpenAlex ID: W2095441731
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description: scientific article; zbMATH DE number 4120157