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Cross-wired lamplighter groups
- Source :
- New York J. Math. 18 (2012) 667-677
- Publication Year :
- 2012
-
Abstract
- We give a necessary and sufficient condition for a locally compact group to be isomorphic to a closed cocompact subgroup in the isometry group of a Diestel-Leader graph. As a consequence of this condition, we see that every cocompact lattice in the isometry group of a Diestel-Leader graph admits a transitive, proper action on some other Diestel-Leader graph. We also give some examples of lattices that are not virtually lamplighters. This implies the class of discrete groups commensurable to lamplighter groups is not closed under quasi-isometries and, combined with work of Eskin, Fisher and Whyte, gives a characterization of their quasi-isometry class.<br />Comment: 11 pages, no figure
- Subjects :
- Mathematics - Group Theory
05C63 (primary), 20E22 (secondary)
Subjects
Details
- Database :
- arXiv
- Journal :
- New York J. Math. 18 (2012) 667-677
- Publication Type :
- Report
- Accession number :
- edsarx.1206.0449
- Document Type :
- Working Paper