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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| Format: | Article |
| Language: | English |
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Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202013078 |
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| _version_ | 1850165733523193856 |
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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 |
| id | doaj-art-e860ea3fd6f14c669ddadbcbfbc14a04 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| 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 |