Small generated groups (Q2710541)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Small generated groups |
scientific article |
Statements
9 October 2001
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infinite groups
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small subsets
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locally compact groups
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solvable groups
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free groups
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large subsets
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topological groups
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Small generated groups (English)
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\textit{A. Bella} and the first author of this paper started [in Quest. Answers Gen. Topology 17, No. 2, 183-197 (1999; Zbl 0966.54001)] an intensive investigation of small and large subsets of infinite groups. The aim of this paper is the study of the class of small generated infinite groups \(G\), that is when \(G\) admits a set of generators which is small. The authors show among other things that every free resp. solvable group is small generated. Concerning topological groups the authors obtain the following interesting result: If a non-metrizable group \(G\) is locally compact and \(\sigma\)-compact, then it is small generated. It remains open if any group, in particular any compact group, is small generated.
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