Abstract
Strongly bounded groups are those groups for which every action by isometries on a metric space has orbits of finite diameter. Many groups have been shown to have this property, and all the known infinite examples so far have cardinality at least 2ℵ0. We produce examples of strongly bounded groups of many cardinalities, including ℵ1, answering a question of Yves de Cornulier [Comm. Algebra 34 (2006), no. 7, 2337–2345]. In fact, any infinite group embeds as a subgroup of a strongly bounded group which is, at most, two cardinalities larger.
| Original language | English |
|---|---|
| Pages (from-to) | 5045-5057 |
| Number of pages | 13 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 148 |
| Issue number | 12 |
| DOIs | |
| State | Published - Dec 2020 |
Bibliographical note
Publisher Copyright:© 2020 American Mathematical Society
Keywords
- Bergman property
- Isometric action
- Small cancellation over free product
- Strong uncountable cofinality
- Strongly bounded group
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