Powers of a product of commutators as products of squares. (Q1774667)

Summary: We prove that for any odd integer \(N\) and any integer \(n>0\), the \(N\)-th power of a product of \(n\) commutators in a nonabelian free group of countable infinite rank can be expressed as a product of squares of \(2n+1\) elements and, for all such odd \(N\) and integers \(n\), there are commutators for which the number \(2n+1\) of squares is the minimum number such that the \(N\)-th power of its product can be written as a product of squares. This generalizes a recent result of \textit{M. Akhavan-Malayeri} [Int. J. Math. Math. Sci. 31, No. 10, 635-637 (2002; Zbl 1013.20028)].