{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T14:42:25Z","timestamp":1648737745456},"reference-count":0,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[1997,12]]},"abstract":"<jats:p> Grigorchuk and Kurchanov's conjecture states that, up to natural equivalence, there is precisely one splitting epimorphism F<jats:sub>2n<\/jats:sub>\u2192F<jats:sub>n<\/jats:sub>\u00d7F<jats:sub>n<\/jats:sub> from a free group F<jats:sub>2n<\/jats:sub> onto F<jats:sub>n<\/jats:sub>\u00d7F<jats:sub>n<\/jats:sub>. The [Formula: see text]-conjecture, while formally similar to the the Poincar\u00e9 conjecture, implies the well-known Andrews\u2013Curtis conjecture about the balanced presentations of the trivial group. In this paper we undertake the task of fully analyzing the [Formula: see text]-conjecture modulo the second commutator subgroup F<jats:sub>2n<\/jats:sub>\u2033. We derive some consequences for the general [Formula: see text]-conjecture. <\/jats:p>","DOI":"10.1142\/s0218196797000307","type":"journal-article","created":{"date-parts":[[2003,10,20]],"date-time":"2003-10-20T20:36:45Z","timestamp":1066682205000},"page":"697-711","source":"Crossref","is-referenced-by-count":2,"title":["Splitting Epimorphisms of Free Metabelian Groups"],"prefix":"10.1142","volume":"07","author":[{"given":"C. K.","family":"Gupta","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G. A.","family":"Noskov","sequence":"additional","affiliation":[{"name":"Institute of Information Technology and Applied Mathematics, Andrianova 28, Omsk 644077, Russia"}],"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\/S0218196797000307","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T17:54:40Z","timestamp":1565114080000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196797000307"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997,12]]},"references-count":0,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[1997,12]]}},"alternative-id":["10.1142\/S0218196797000307"],"URL":"https:\/\/doi.org\/10.1142\/s0218196797000307","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[1997,12]]}}}