{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T14:22:28Z","timestamp":1775830948092,"version":"3.50.1"},"reference-count":19,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2006,2]]},"abstract":"<jats:p> Let G be a group hyperbolic relative to a collection of subgroups {H<jats:sub>\u03bb<\/jats:sub>, \u03bb \u2208 \u039b}. We say that a subgroup Q \u2264 G is hyperbolically embedded into G, if G is hyperbolic relative to {H<jats:sub>\u03bb<\/jats:sub>, \u03bb \u2208 \u039b} \u222a {Q}. In this paper we obtain a characterization of hyperbolically embedded subgroups. In particular, we show that if an element g \u2208 G has infinite order and is not conjugate to an element of some H<jats:sub>\u03bb<\/jats:sub>, \u03bb \u2208 \u039b, then the (unique) maximal elementary subgroup containing g is hyperbolically embedded into G. This allows us to prove that if G is boundedly generated, then G is elementary or H<jats:sub>\u03bb<\/jats:sub> = G for some \u03bb \u2208 \u039b. <\/jats:p>","DOI":"10.1142\/s0218196706002901","type":"journal-article","created":{"date-parts":[[2006,3,8]],"date-time":"2006-03-08T10:49:22Z","timestamp":1141814962000},"page":"99-118","source":"Crossref","is-referenced-by-count":48,"title":["ELEMENTARY SUBGROUPS OF RELATIVELY HYPERBOLIC GROUPS AND BOUNDED GENERATION"],"prefix":"10.1142","volume":"16","author":[{"given":"DENIS V.","family":"OSIN","sequence":"first","affiliation":[{"name":"Department of Mathematics, The City College of New York, 138th Street and Convent Ave., New York, NY 10031, USA"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196792000220"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-95-07709-6"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-12494-9"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.2307\/2374319"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/S0764-4442(01)02061-4"},{"key":"rf8","first-page":"810","volume":"8","author":"Farb B.","journal-title":"GAFA"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/54.2.261"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-9167-8"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-9586-7_3"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-96-01510-3"},{"key":"rf13","unstructured":"M. V.\u00a0Kumar, Number Theory, Halifax, NS, 1994, CMS Conference Proceedings\u00a015 (Amer. Math. Soc., Providence, RI, 1995)\u00a0pp. 249\u2013261."},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-8965-0"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61896-3"},{"key":"rf17","first-page":"543","volume":"182","author":"Olshanskii A. Yu.","journal-title":"Mat. Sbornik"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196793000251"},{"key":"rf19","volume":"179","author":"Osin D. V.","journal-title":"Memoirs Amer. Math. Soc."},{"key":"rf21","first-page":"1327","volume":"314","author":"Rapinchuk A. S.","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.1007\/BF02698832"},{"key":"rf23","first-page":"97","volume":"54","author":"Tavgen' I. O.","journal-title":"Izv. Akad. Nauk SSSR Ser. Mat."}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196706002901","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T22:25:57Z","timestamp":1565130357000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196706002901"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,2]]},"references-count":19,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2006,2]]}},"alternative-id":["10.1142\/S0218196706002901"],"URL":"https:\/\/doi.org\/10.1142\/s0218196706002901","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,2]]}}}