Powers of a product of commutators as products of squares. (14th February 2004)

• Record Type: Journal Article
• Authors: Abdollahi, Alireza
• Is Part Of: International journal of mathematics and mathematical sciences. Number 7(2004)
• Page Start: 373
• Page End: 375
• Publication Date: 2004-02-14
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1155/S0161171204304047
• Languages: English
• ISSNs: 0161-1712

Abstract

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.