Powers of a product of commutators as products of squares. (14th February 2004) - Abdollahi, Alireza
Abstract : We prove that for any odd integerN and any integern > 0, theN th power of a product ofn commutators in a nonabelian free group of countable infinite rank can be expressed as a product of squares of2 n + 1 elements and, for all such oddN and integersn, there are commutators for which the number2 n + 1 of squares is the minimum number such that theN th power of its product can be written as a product of squares. This generalizes a recent result of Akhavan-Malayeri.