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- Title
Hyperbolic structures on wreath products.
- Authors
H. Balasubramanya, Sahana
- Abstract
The study of the poset of hyperbolic structures on a group G was initiated by C. Abbott, S. Balasubramanya and D. Osin, [Hyperbolic structures on groups, Algebr. Geom. Topol. 19 2019, 4, 1747–1835, 10.2140/agt.2019.19.1747]. However, this poset is still very far from being understood, and several questions remain unanswered. In this paper, we give a complete description of the poset of hyperbolic structures on the lamplighter groups wr ℤnℤ and obtain some partial results about more general wreath products. As a consequence of this result, we answer two open questions regarding quasi-parabolic structures: we give an example of a group G with an uncountable chain of quasi-parabolic structures and prove that the lamplighter groups wr ℤnℤ all have finitely many quasi-parabolic structures.
- Subjects
HYPERBOLOID structures; HYPERBOLIC groups; OPEN-ended questions; MANUFACTURED products; WREATH products (Group theory)
- Publication
Journal of Group Theory, 2020, Vol 23, Issue 2, p357
- ISSN
1433-5883
- Publication type
Article
- DOI
10.1515/jgth-2018-0176