Elementary properties of linear groups and related problems.
type: Item
instance of: scholarly article
title: Elementary properties of linear groups and related problems.
zbMATH Open document ID: 1077.20059
author: E. I. Bunina
author: A. V. Mikhalev
published in: Journal of Mathematical Sciences (New York)
publication date: 2005-06-07T00:00:00Z
review text: The paper under review is a survey devoted to main results on elementary properties of groups with the main focus on linear groups. Section 1 contains necessary information about model theory. Results presented in Section 2 are devoted to the classification of groups up to their elementary properties. Section 3 contains results on elementary classification of classical linear groups. Section 4 is devoted to other results on the elementary equivalence of groups and related structures, in particular, of the lattices of subalgebras of free algebras of varieties, of modules and their tensor products, free products of groups, filtered and wreath products. Section 5 is devoted to categoricity and stability. In particular it contains results on \(\varpi\)-categorical, \(\varpi\)-stable and \(\varpi_1\)-categorical groups. Section 6 contains results on decidable and undecidable group theories.
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 20A15
Mathematics Subject Classification ID: 03C60
Mathematics Subject Classification ID: 20E10
Mathematics Subject Classification ID: 20F10
Mathematics Subject Classification ID: 03C45
Mathematics Subject Classification ID: 03D40
zbMATH DE Number: 2174286
zbMATH Keywords: linear groups
zbMATH Keywords: elementary properties
zbMATH Keywords: survey
zbMATH Keywords: elementary equivalences
MaRDI profile type: Publication
DOI: 10.1023/B:JOTH.0000036655.73484.A8
description: scientific article; zbMATH DE number 2174286