Powers of commutators as products of squares

Let F be a free group and x,y be two distinct elements of a free generating set, then [x,y] n is not a product of two squares in F, and it is the product of three squares. We give a short combinatorial proof.

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Main Author: M. Akhavan-Malayeri
Format: Article
Language:English
Published: Wiley 2002-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/S0161171202013078
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author M. Akhavan-Malayeri
author_facet M. Akhavan-Malayeri
author_sort M. Akhavan-Malayeri
collection DOAJ
description Let F be a free group and x,y be two distinct elements of a free generating set, then [x,y] n is not a product of two squares in F, and it is the product of three squares. We give a short combinatorial proof.
format Article
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institution OA Journals
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1687-0425
language English
publishDate 2002-01-01
publisher Wiley
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series International Journal of Mathematics and Mathematical Sciences
spelling doaj-art-e860ea3fd6f14c669ddadbcbfbc14a042025-08-20T02:21:38ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-01311063563710.1155/S0161171202013078Powers of commutators as products of squaresM. Akhavan-Malayeri0Azzahra University, Vanak, Tehran 19834, IranLet F be a free group and x,y be two distinct elements of a free generating set, then [x,y] n is not a product of two squares in F, and it is the product of three squares. We give a short combinatorial proof.http://dx.doi.org/10.1155/S0161171202013078
spellingShingle M. Akhavan-Malayeri
Powers of commutators as products of squares
International Journal of Mathematics and Mathematical Sciences
title Powers of commutators as products of squares
title_full Powers of commutators as products of squares
title_fullStr Powers of commutators as products of squares
title_full_unstemmed Powers of commutators as products of squares
title_short Powers of commutators as products of squares
title_sort powers of commutators as products of squares
url http://dx.doi.org/10.1155/S0161171202013078
work_keys_str_mv AT makhavanmalayeri powersofcommutatorsasproductsofsquares