TY - JOUR
T1 - Hierarchy for groups acting on hyperbolic ℤn-spaces
AU - Grecianu, Andrei Paul
AU - Myasnikov, Alexei
AU - Serbin, Denis
N1 - Publisher Copyright:
© 2021 World Scientific Publishing Company
PY - 2021/12/1
Y1 - 2021/12/1
N2 - In [A.-P. Grecianu, A. Kvaschuk, A. G. Myasnikov and D. Serbin, Groups acting on hyperbolic Λ-metric spaces, Int. J. Algebra Comput. 25(6) (2015) 977–1042], the authors initiated a systematic study of hyperbolic Λ-metric spaces, where Λ is an ordered abelian group, and groups acting on such spaces. The present paper concentrates on the case Λ = ℤn taken with the right lexicographic order and studies the structure of finitely generated groups acting on hyperbolic ℤn-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 : (AMS-209), Annals of Mathematics Studies (Princeton University Press, 2021)]) similar to the one established for ℤn-free groups in [O. Kharlampovich, A. G. Myasnikov, V. N. Remeslennikov and D. Serbin, Groups with free regular length functions in ℤn, Trans. Amer. Math. Soc. 364 (2012) 2847–2882].
AB - In [A.-P. Grecianu, A. Kvaschuk, A. G. Myasnikov and D. Serbin, Groups acting on hyperbolic Λ-metric spaces, Int. J. Algebra Comput. 25(6) (2015) 977–1042], the authors initiated a systematic study of hyperbolic Λ-metric spaces, where Λ is an ordered abelian group, and groups acting on such spaces. The present paper concentrates on the case Λ = ℤn taken with the right lexicographic order and studies the structure of finitely generated groups acting on hyperbolic ℤn-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 : (AMS-209), Annals of Mathematics Studies (Princeton University Press, 2021)]) similar to the one established for ℤn-free groups in [O. Kharlampovich, A. G. Myasnikov, V. N. Remeslennikov and D. Serbin, Groups with free regular length functions in ℤn, Trans. Amer. Math. Soc. 364 (2012) 2847–2882].
KW - Hyperbolic group
KW - None
KW - group action
KW - hyperbolic space
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U2 - 10.1142/S0218196721500612
DO - 10.1142/S0218196721500612
M3 - Article
AN - SCOPUS:85119925990
SN - 0218-1967
VL - 31
SP - 1663
EP - 1690
JO - International Journal of Algebra and Computation
JF - International Journal of Algebra and Computation
IS - 8
ER -