Commutator length and square length of the wreath product of a free group by the infinite cyclic group. (English) Zbl 1004.20017

Akhavan-Malayeri, Mehri

Houston J. Math. 27, No. 4, 753-756 (2001).

Let \(W=G\wr C_\infty\), the wreath product of a group \(G\) and the infinite cyclic group. The author shows how to express every element of the commutator subgroup \(W'\) as a product of at most three commutators. She also shows how to express every element of \(W^2=\langle x^2,\;x\in W\rangle\) as a product of at most seven squares in \(W\).

Reviewer: Akbar H.Rhemtulla (Edmonton)

MSC:

20E22	Extensions, wreath products, and other compositions of groups
20F12	Commutator calculus

Keywords:

wreath products; commutator lengths; square lengths; commutator subgroups; products of commutators; products of squares