{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T04:54:49Z","timestamp":1777438489182,"version":"3.51.4"},"reference-count":11,"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":[[2001,4]]},"abstract":"<jats:p> We consider the following property for a group G:(RZ<jats:sub>n<\/jats:sub>)ifH<jats:sub>1<\/jats:sub>,\u2026,H<jats:sub>n<\/jats:sub>are finitely generated subgroups of G then the setH<jats:sub>1<\/jats:sub> H<jats:sub>2<\/jats:sub>\u22ef H<jats:sub>n<\/jats:sub>= {h<jats:sub>1<\/jats:sub> \u22ef h<jats:sub>n<\/jats:sub>| h<jats:sub>1<\/jats:sub>\u2208 H<jats:sub>1<\/jats:sub>, \u2026,h<jats:sub>n<\/jats:sub>\u2208 H<jats:sub>n<\/jats:sub>}is closed with respect to the profinite topology of G. It is obvious that finite groups and finitely generated commutative groups have the property ( RZ <jats:sub>n<\/jats:sub>). L. Ribes and P. Zalesski\u012d proved that any free group has ( RZ <jats:sub>n<\/jats:sub>). We show that the property ( RZ <jats:sub>n<\/jats:sub>) is stable under the free product operation. We use techniques developed by B. Herwig and D. Lascar on the one hand, R. Gitik on the other hand. <\/jats:p>","DOI":"10.1142\/s0218196701000449","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T11:05:36Z","timestamp":1027767936000},"page":"171-184","source":"Crossref","is-referenced-by-count":15,"title":["FREE PRODUCT, PROFINITE TOPOLOGY AND FINITELY GENERATED SUBGROUPS"],"prefix":"10.1142","volume":"11","author":[{"given":"THIERRY","family":"COULBOIS","sequence":"first","affiliation":[{"name":"\u00c9quipe de Logique Math\u00e9matique, Universit\u00e9 Paris 7, 2 place Jussieu, 75251 Paris Cedex 05, France"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700009824"},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1996.6847"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-7.1.29"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1949-0032642-4"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.2307\/1969513"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1007\/BF01299742"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-99-02374-0"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1007\/BF01305233"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/23.4.356"},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/25.1.37"},{"key":"p_11","first-page":"1324","volume":"33","author":"Romanovski N.","year":"1969","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\/S0218196701000449","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T13:19:20Z","timestamp":1565183960000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196701000449"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,4]]},"references-count":11,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2001,4]]}},"alternative-id":["10.1142\/S0218196701000449"],"URL":"https:\/\/doi.org\/10.1142\/s0218196701000449","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,4]]}}}