On commutator length and square length of the wreath product of a group by a finitely generated Abelian group. (English) Zbl 1203.20034

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)].


20F12 Commutator calculus
20E22 Extensions, wreath products, and other compositions of groups
20F05 Generators, relations, and presentations of groups


Zbl 1004.20017
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[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
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