This article is cited in 17 papers

Elementary Classes of Groups

D. V. Osin

Budget and Treasury Academy, Ministry of Finance of the Russian Federation

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.

UDC: 512.54

Received: 22.10.2001

DOI: 10.4213/mzm406

 English version: Mathematical Notes, 2002, 72:1, 75–82

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