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Hierarchy for groups acting on hyperbolic ℤn-spaces
- Source :
- International Journal of Algebra and Computation. 31:1663-1690
- Publication Year :
- 2021
- Publisher :
- World Scientific Pub Co Pte Ltd, 2021.
-
Abstract
- In [A.-P. Grecianu, A. Kvaschuk, A. G. Myasnikov and D. Serbin, Groups acting on hyperbolic [Formula: see text]-metric spaces, Int. J. Algebra Comput. 25(6) (2015) 977–1042], the authors initiated a systematic study of hyperbolic [Formula: see text]-metric spaces, where [Formula: see text] is an ordered abelian group, and groups acting on such spaces. The present paper concentrates on the case [Formula: see text] taken with the right lexicographic order and studies the structure of finitely generated groups acting on hyperbolic [Formula: see text]-metric spaces. Under certain constraints, the structure of such groups is described in terms of a hierarchy (see [D. T. Wise, The Structure of Groups with a Quasiconvex Hierarchy[Formula: see text] [Formula: see text]AMS-[Formula: see text], Annals of Mathematics Studies (Princeton University Press, 2021)]) similar to the one established for [Formula: see text]-free groups in [O. Kharlampovich, A. G. Myasnikov, V. N. Remeslennikov and D. Serbin, Groups with free regular length functions in [Formula: see text], Trans. Amer. Math. Soc. 364 (2012) 2847–2882].
Details
- ISSN :
- 17936500 and 02181967
- Volume :
- 31
- Database :
- OpenAIRE
- Journal :
- International Journal of Algebra and Computation
- Accession number :
- edsair.doi...........213d1934c9d2c5438192a4c1d5cfc32b