{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T10:30:46Z","timestamp":1775644246557,"version":"3.50.1"},"reference-count":0,"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":[[1993,3]]},"abstract":"<jats:p> Gr\u00e2ce \u00e0 l\u2019introduction de la notion de forme exponentielle r\u00e9duite, nous montrons l\u2019injectivit\u00e9 de la transformation de Magnus associ\u00e9e au groupe partiellement commutatif libre F(A, \u03d1). Nous en d\u00e9duisons la s\u00e9paration de la topologie p-adique de F(A, \u03d1), l\u2019existence de plus petites racines dans F(A, \u03d1) et enfin la structure des centralisateurs dans F(A, \u03d1). <\/jats:p><jats:p> We introduce the notion of reduced exponential form in the free partially commutative group F(A, \u03d1). This allows us to prove that the Magnus transformation associated with F(A, \u03d1) is injective. We deduce from this result that the p-adic topology on F(A, \u03d1) is Hausdorff, that there exist least roots in F(A, \u03d1) and finally the exact structure of centralizers in F(A, \u03d1). <\/jats:p>","DOI":"10.1142\/s0218196793000032","type":"journal-article","created":{"date-parts":[[2004,11,22]],"date-time":"2004-11-22T22:29:30Z","timestamp":1101162570000},"page":"15-41","source":"Crossref","is-referenced-by-count":19,"title":["PARTIALLY COMMUTATIVE MAGNUS TRANSFORMATIONS"],"prefix":"10.1142","volume":"03","author":[{"given":"G.","family":"DUCHAMP","sequence":"first","affiliation":[{"name":"Universit\u00e9 Paris 6, Universit\u00e9 de Rouen and CNRS(LITP), France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"D.","family":"KROB","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Paris 6, Universit\u00e9 de Rouen and CNRS(LITP), France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196793000032","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T09:20:55Z","timestamp":1565169655000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196793000032"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,3]]},"references-count":0,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[1993,3]]}},"alternative-id":["10.1142\/S0218196793000032"],"URL":"https:\/\/doi.org\/10.1142\/s0218196793000032","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,3]]}}}