{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T06:11:23Z","timestamp":1777615883389,"version":"3.51.4"},"reference-count":17,"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":[[2014,8]]},"abstract":"<jats:p> In [Bardakov and Gongopadhyay, Palindromic width of free nilpotent groups, J. Algebra\u00a0402 (2014) 379\u2013391] the authors provided a bound for the palindromic widths of free abelian-by-nilpotent group AN<jats:sub>n<\/jats:sub> of rank n and free nilpotent group N <jats:sub>n,r<\/jats:sub> of rank n and step r. In the present paper, we study palindromic widths of groups [Formula: see text] and [Formula: see text]. We denote by [Formula: see text] the quotient of the group G<jats:sub>n<\/jats:sub> = \u3008x<jats:sub>1<\/jats:sub>, \u2026, x<jats:sub>n<\/jats:sub>\u3009, which is free in some variety by the normal subgroup generated by [Formula: see text]. We prove that the palindromic width of the quotient [Formula: see text] is finite and bounded by 3n. We also prove that the palindromic width of the quotient [Formula: see text] is precisely 2(n - 1). As a corollary to this result, we improve the lower bound of the palindromic width of N <jats:sub>n,r<\/jats:sub>. We also improve the bound of the palindromic width of a free metabelian group. We prove that the palindromic width of a free metabelian group of rank n is at most 4n - 1. <\/jats:p>","DOI":"10.1142\/s0218196714500246","type":"journal-article","created":{"date-parts":[[2014,7,2]],"date-time":"2014-07-02T06:58:05Z","timestamp":1404284285000},"page":"553-567","source":"Crossref","is-referenced-by-count":9,"title":["On palindromic width of certain extensions and quotients of free nilpotent groups"],"prefix":"10.1142","volume":"24","author":[{"given":"Valeriy G.","family":"Bardakov","sequence":"first","affiliation":[{"name":"Sobolev Institute of Mathematics, Novosibirsk State University, Novisibirsk 630090, Russia"},{"name":"Laboratory of Quantum Topology, Chelyabinsk State University, Brat\u00e9v Kashirinykh Street 129, Chelyabinsk 454001, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Krishnendu","family":"Gongopadhyay","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Knowledge City, Sector 81, S.A.S. Nagar, P.O. Manauli 140306, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2014,9,3]]},"reference":[{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1017\/S0017089500032407"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2013.12.002"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2004.11.003"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700015822"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.2307\/2374319"},{"key":"rf7","unstructured":"D.\u00a0Collins, Combinatorial and Geometric Group Theory, London Mathematical Society Lecture Note Series\u00a0204 (Cambridge University Press, Cambridge, 1995)\u00a0pp. 63\u201372."},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1142\/S0218216510007802"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.4310\/AJM.2008.v12.n1.a5"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/s000140050143"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1090\/S1088-4173-09-00191-X"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2011.02.010"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1999.8117"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2008.09.011"},{"key":"rf16","volume-title":"Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations","author":"Magnus W.","year":"1996"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2005.12.005"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1969-126-4"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1080\/00927879708825944"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196714500246","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T20:29:06Z","timestamp":1565123346000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196714500246"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,8]]},"references-count":17,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2014,9,3]]},"published-print":{"date-parts":[[2014,8]]}},"alternative-id":["10.1142\/S0218196714500246"],"URL":"https:\/\/doi.org\/10.1142\/s0218196714500246","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,8]]}}}