Products of commutators of unipotent matrices of index 2 in \(\mathrm{GL}_n(\mathbb{H})\). (English) Zbl 07903868
Summary: The aim of this paper is to show that if \(\mathbb{H}\) is the real quaternion division ring and \(n\) is an integer greater than 1, then every matrix in the special linear group \(\mathrm{SL}_n(\mathbb{H})\) can be expressed as a product of at most three commutators of unipotent matrices of index 2.
MSC:
| 15B33 | Matrices over special rings (quaternions, finite fields, etc.) |
| 15A23 | Factorization of matrices |
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| [27] | Nguyen Thi Thai Ha Faculty of Mathematics and Computer Science University of Science, Ho Chi Minh City, Vietnam Vietnam National University, Ho Chi Minh City, Vietnam Campus in Ho Chi Minh City, University of Transport and Communications Ho Chi Minh City, Vietnam e-mail: hantt ph@utc.edu.vn |
| [28] | Dao Trong Toan (Corresponding Author) Faculty of Mathematics and Computer Science University of Science, Ho Chi Minh City, Vietnam Vietnam National University, Ho Chi Minh City, Vietnam e-mail: daotrongtoan.dtt4@gmail.com |
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