Akhavan-Malayeri, Mehri On commutator length and square length of the wreath product of a group by a finitely generated Abelian group. (English) Zbl 1203.20034 Algebra Colloq. 17, Spec. Iss. 1, 799-802 (2010). Summary: Let \(W=G\wr H\) be the wreath product of \(G\) by an \(n\)-generator Abelian group \(H\). We prove that every element of \(W'\) is a product of at most \(n+2\) commutators, and every element of \(W^2\) is a product of at most \(3n+4\) squares in \(W\). This generalizes our previous result [in Houston J. Math. 27, No. 4, 753-756 (2001; Zbl 1004.20017)]. Cited in 3 Documents MSC: 20F12 Commutator calculus 20E22 Extensions, wreath products, and other compositions of groups 20F05 Generators, relations, and presentations of groups Keywords:commutator lengths; wreath products; commutators in groups; squares in groups; products of squares; commutator subgroup; products of commutators Citations:Zbl 1004.20017 PDF BibTeX XML Cite \textit{M. Akhavan-Malayeri}, Algebra Colloq. 17, 799--802 (2010; Zbl 1203.20034) Full Text: DOI Link References: [1] Akhavan-Malayeri M., Houston J. Math. 27 pp 753– [2] Bardakov V. G., Algebra and Logic 36 pp 494– [3] DOI: 10.1017/S1446788700002743 · Zbl 0991.20023 [4] DOI: 10.1006/jabr.2001.9137 · Zbl 1004.20012 [5] DOI: 10.1090/S0002-9939-1973-0314997-5 [6] DOI: 10.1017/S0305004100043231 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.