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Elementary Classes of Groups

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Abstract

Let \(B\) be a class of groups. The elementary class with base \(B\) is defined as the minimal class of groups containing \(B\) and closed with respect to taking subgroups, quotient groups, group extensions, and direct limits. Properties of such classes are studied. Some applications to the theory of elementary amenable groups and a relation to the Kurosh--Chernikov classes of generalized solvable groups are considered.

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  1. Academy of Budget and Finances, Ministry of Finances of the Russian Federation, Russia

    D. V. Osin

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  1. D. V. Osin
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Osin, D.V. Elementary Classes of Groups. Mathematical Notes 72, 75–82 (2002). https://doi.org/10.1023/A:1019869105364

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  • DOI: https://doi.org/10.1023/A:1019869105364

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