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Length functions on groups and actions on graphs.
- Source :
-
Communications in Algebra . 2024, Vol. 52 Issue 6, p2269-2281. 13p. - Publication Year :
- 2024
-
Abstract
- We study generalizations of Chiswell's theorem that 0-hyperbolic Lyndon length functions on groups always arise as based length functions of the group acting isometrically on a tree. We produce counter-examples to show that this Theorem fails if one replaces 0-hyperbolicity with δ-hyperbolicity. We then propose a set of axioms for the length function on a finitely generated group that ensures the function is bi-Lipschitz equivalent to a (or any) length function of the group acting on its Cayley graph with respect to some finite generating set. [ABSTRACT FROM AUTHOR]
- Subjects :
- *CAYLEY graphs
*AXIOMS
Subjects
Details
- Language :
- English
- ISSN :
- 00927872
- Volume :
- 52
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Communications in Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 176474995
- Full Text :
- https://doi.org/10.1080/00927872.2023.2296887