{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T13:41:56Z","timestamp":1775828516794,"version":"3.50.1"},"reference-count":11,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[1999,10]]},"abstract":"<jats:p> A subgroup H of a free product [Formula: see text] of groups G<jats:sub>\u03b1<\/jats:sub>, \u03b1\u2208 I, is called factor free if for every [Formula: see text] and \u03b2\u00a0\u2208\u00a0I one has S\u00a0H\u00a0S<jats:sup>-1<\/jats:sup>\u2229 G<jats:sub>\u03b2<\/jats:sub> = {1} (by Kurosh theorem on subgroups of free products, factor free subgroups are free). If K is a finitely generated free group, denote [Formula: see text], where r(K) is the rank of K. It is proven that if H, K are finitely generated factor free subgroups of a free product [Formula: see text] then [Formula: see text]. It is also shown that the inequality [Formula: see text] of Hanna Neumann conjecture on subgroups of free groups does not hold for factor free subgroups of free products. <\/jats:p>","DOI":"10.1142\/s021819679900031x","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T07:05:54Z","timestamp":1027753554000},"page":"521-528","source":"Crossref","is-referenced-by-count":11,"title":["ON THE INTERSECTION OF FINITELY GENERATED SUBGROUPS IN FREE PRODUCTS OF GROUPS"],"prefix":"10.1142","volume":"09","author":[{"given":"S. V.","family":"IVANOV","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Illinois at Urbana\u2013Champaign, 1409 West Green Street, Urbana, IL\u00a061801, USA"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s1-29.4.428"},{"key":"p_3","first-page":"186","volume":"4","author":"Neumann H.","year":"1956","journal-title":"Publ. Math."},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-1986-033-x"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1007\/BF01232249"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1007\/BF02095994"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0069177"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1007\/BF01162012"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1007\/BF02100597"},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1007\/BF01232368"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s1-41.1.673"},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1017\/S0004972700009291"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021819679900031X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T17:55:51Z","timestamp":1565114151000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021819679900031X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,10]]},"references-count":11,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[1999,10]]}},"alternative-id":["10.1142\/S021819679900031X"],"URL":"https:\/\/doi.org\/10.1142\/s021819679900031x","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,10]]}}}