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Powers of a product of commutators as products of squares

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  • Alireza Abdollahi

Abstract

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 2 n + 1 elements and, for all such odd N and integers n , there are commutators for which the number 2 n + 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 Akhavan-Malayeri.

Suggested Citation

  • Alireza Abdollahi, 2004. "Powers of a product of commutators as products of squares," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-3, January.
    • Handle: RePEc:hin:jijmms:905349
    DOI: 10.1155/S0161171204304047
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