Powers of a product of commutators as products of squares
We prove that for any odd integer N and any integer n>0, the Nth 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 2n+1 elements and, for all such odd N and integers n, there are commutators for which the number...
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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204304047 |
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| _version_ | 1832564098463694848 |
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| author | Alireza Abdollahi |
| author_facet | Alireza Abdollahi |
| author_sort | Alireza Abdollahi |
| collection | DOAJ |
| description | We prove that for any odd integer N and any integer n>0, the Nth 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 2n+1 elements and, for all such odd N and integers n, there are commutators for which the number 2n+1 of squares is the minimum number such that the Nth power of its product can be written as a product of squares. This generalizes a recent result of Akhavan-Malayeri. |
| format | Article |
| id | doaj-art-0121772187004c2194af3496643ab841 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-0121772187004c2194af3496643ab8412025-02-03T01:11:47ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004737337510.1155/S0161171204304047Powers of a product of commutators as products of squaresAlireza Abdollahi0Department of Mathematics, University of Isfahan, Isfahan 81746-73441, IranWe prove that for any odd integer N and any integer n>0, the Nth 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 2n+1 elements and, for all such odd N and integers n, there are commutators for which the number 2n+1 of squares is the minimum number such that the Nth power of its product can be written as a product of squares. This generalizes a recent result of Akhavan-Malayeri.http://dx.doi.org/10.1155/S0161171204304047 |
| spellingShingle | Alireza Abdollahi Powers of a product of commutators as products of squares International Journal of Mathematics and Mathematical Sciences |
| title | Powers of a product of commutators as products of squares |
| title_full | Powers of a product of commutators as products of squares |
| title_fullStr | Powers of a product of commutators as products of squares |
| title_full_unstemmed | Powers of a product of commutators as products of squares |
| title_short | Powers of a product of commutators as products of squares |
| title_sort | powers of a product of commutators as products of squares |
| url | http://dx.doi.org/10.1155/S0161171204304047 |
| work_keys_str_mv | AT alirezaabdollahi powersofaproductofcommutatorsasproductsofsquares |