{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T12:27:19Z","timestamp":1648643239934},"reference-count":16,"publisher":"World Scientific Pub Co Pte Ltd","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2021,12]]},"abstract":"<jats:p> 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.\u00a025(6) (2015) 977\u20131042], 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.\u00a0364 (2012) 2847\u20132882]. <\/jats:p>","DOI":"10.1142\/s0218196721500612","type":"journal-article","created":{"date-parts":[[2021,11,7]],"date-time":"2021-11-07T04:19:30Z","timestamp":1636258770000},"page":"1663-1690","source":"Crossref","is-referenced-by-count":0,"title":["Hierarchy for groups acting on hyperbolic \u2124n-spaces"],"prefix":"10.1142","volume":"31","author":[{"given":"Andrei-Paul","family":"Grecianu","sequence":"first","affiliation":[{"name":"Department of Mathematics, St. Laurent College, 625 Sainte Croix Ave, Montreal H4L 3X7, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexei","family":"Myasnikov","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Stevens Institute of Technology, 1 Castle Point on Hudson, Hoboken, NJ 07030, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Denis","family":"Serbin","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Stevens Institute of Technology, 1 Castle Point on Hudson, Hoboken, NJ 07030, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2021,11,6]]},"reference":[{"key":"S0218196721500612BIB001","doi-asserted-by":"publisher","DOI":"10.1515\/9781400882083-017"},{"key":"S0218196721500612BIB002","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100053093"},{"key":"S0218196721500612BIB003","doi-asserted-by":"publisher","DOI":"10.1142\/4495"},{"key":"S0218196721500612BIB004","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511565878"},{"key":"S0218196721500612BIB005","doi-asserted-by":"publisher","DOI":"10.2140\/gt.2003.7.933"},{"key":"S0218196721500612BIB006","volume-title":"Espaces Metriques Hyperboliques sur les Groupes Hyperboliques d\u2019apr\u00e8s Michael Gromov","author":"Ghys E.","year":"1991"},{"key":"S0218196721500612BIB008","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196715500289"},{"key":"S0218196721500612BIB009","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196707003330"},{"key":"S0218196721500612BIB010","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-2012-05376-1"},{"key":"S0218196721500612BIB012","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196713400031"},{"key":"S0218196721500612BIB013","doi-asserted-by":"publisher","DOI":"10.7146\/math.scand.a-10684"},{"key":"S0218196721500612BIB014","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-3443-9_8"},{"key":"S0218196721500612BIB015","doi-asserted-by":"publisher","DOI":"10.2307\/1971082"},{"key":"S0218196721500612BIB016","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/378\/07010"},{"key":"S0218196721500612BIB017","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-51.3.449"},{"key":"S0218196721500612BIB018","series-title":"Annals of Mathematics Studies","volume-title":"The Structure of Groups with a Quasiconvex Hierarchy AMS-","author":"Wise D. 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