Tame minimal simple groups of finite Morley rank
type: Item
instance of: scholarly article
title: Tame minimal simple groups of finite Morley rank
zbMATH Open document ID: 1056.20020
author: Gregory Cherlin
author: Eric Jaligot
published in: Journal of Algebra
publication date: 2004-10-01T00:00:00Z
review text: The paper is a contribution to the program aiming to prove the Cherlin-Zil'ber algebraicity conjecture: any infinite simple group of finite Morley rank is an algebraic group over an algebraically closed field. A group of finite Morley rank is said to be tame if does not interpret a bad field naturally. A simple group of finite Morley rank is called minimal simple if all its proper definable connected subgroups are solvable. A group of finite Morley rank is said to be of odd type if the connected component of any Sylow 2-subgroup of it is a nontrivial divisible Abelian 2-group. The main result: in any tame minimal simple group of odd type the Prüfer rank of the connected component of a Sylow 2-subgroup is bounded by 2. -- For the remaining cases, in which the Prüfer rank is 1 or 2, the groups are analyzed from various points of view, notably in terms of Borel subgroups; the potential non-algebraic configurations are delineated with some precision.
Mathematics Subject Classification ID: 20E32
Mathematics Subject Classification ID: 03C45
Mathematics Subject Classification ID: 03C60
Mathematics Subject Classification ID: 20A15
Mathematics Subject Classification ID: 20G15
zbMATH DE Number: 2105404
zbMATH Keywords: groups of finite Morley rank
zbMATH Keywords: infinite minimal simple groups
zbMATH Keywords: Cherlin-Zilber conjecture
reviewed by: Oleg Belegradek
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2003.12.027
OpenAlex ID: W1973235250
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DOI: 10.1016/J.JALGEBRA.2003.12.027
description: scientific article; zbMATH DE number 2105404