{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T12:13:12Z","timestamp":1773231192257,"version":"3.50.1"},"reference-count":8,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2009,3]]},"abstract":"<jats:p> We prove that the amalgamated product of free groups with cyclic amalgamations satisfying certain conditions are virtually free-by-cyclic. In case the cyclic amalgamated subgroups lie outside the derived group such groups are free-by-cyclic. Similarly a one-relator HNN-extension in which the conjugated elements either coincide or are independent modulo the derived group is shown to be free-by-cyclic. In general, the amalgamated product of free groups with cyclic amalgamations is free-by-(torsion-free nilpotent). The special case of the double of a free group amalgamating a cyclic subgroup is shown to be virtually free-by-abelian. Analagous results are obtained for certain one-relator HNN-extensions. <\/jats:p>","DOI":"10.1142\/s0218196709005032","type":"journal-article","created":{"date-parts":[[2009,3,27]],"date-time":"2009-03-27T07:19:21Z","timestamp":1238138361000},"page":"213-227","source":"Crossref","is-referenced-by-count":5,"title":["VIRTUAL PROPERTIES OF CYCLICALLY PINCHED ONE-RELATOR GROUPS"],"prefix":"10.1142","volume":"19","author":[{"given":"GILBERT","family":"BAUMSLAG","sequence":"first","affiliation":[{"name":"Department of Computer Science, City College of New York, Convent Ave. and 138th Street, New York, N.Y. 10031, USA"}]},{"given":"BENJAMIN","family":"FINE","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Fairfield University, 1073 North Benson Road, Fairfield CT 06430-5195, USA"}]},{"suffix":"III","given":"CHARLES F.","family":"MILLER","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of Melbourne, Melbourne 3010,  Australia"}]},{"given":"DOUGLAS","family":"TROEGER","sequence":"additional","affiliation":[{"name":"Department of Computer Science, City College of New York, Convent Ave. and 138th Street, New York, N.Y. 10031, USA"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01195185"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1967-11799-3"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1017\/S0004972700046906"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100060527"},{"key":"rf6","first-page":"457","volume":"166","author":"Dunfield N.","journal-title":"Geom. Topol."},{"key":"rf7","first-page":"1061","volume":"2149","author":"Feighn M.","journal-title":"Ann. Math."},{"key":"rf8","first-page":"421","volume":"1","author":"Hall M.","journal-title":"Canad. J. Math."},{"key":"rf9","first-page":"690","volume":"70","author":"Neumann H.","journal-title":"Amer. J. Math."}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196709005032","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T18:19:27Z","timestamp":1565115567000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196709005032"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,3]]},"references-count":8,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2009,3]]}},"alternative-id":["10.1142\/S0218196709005032"],"URL":"https:\/\/doi.org\/10.1142\/s0218196709005032","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,3]]}}}