Article Sidebar

PDF
Date Published: 30/10/2025
Abstract Views: 160
Views PDF: 4
DOI: 10.54607/hcmue.js.22.10.4764(2025)
Issue
Tập 22, Số 10(2025)
Section
Articles
How to Cite
Nguyen, P. T., Trinh, Q. H., & Nguyen, A. S. (2025). PRODUCTS OF INVOLUTIONS IN THE VERSHIK-KEROV GROUP. Ho Chi Minh City University of Education Journal of Science, 22(10), 1867-1873. https://doi.org/10.54607/hcmue.js.22.10.4764(2025)

PRODUCTS OF INVOLUTIONS IN THE VERSHIK-KEROV GROUP

Nguyen Phu Thinh1, , Trinh Quoc Huy2, Nguyen Anh Sy2
1 Ho Chi Minh City University of Education, Vietnam
2 Trường Đại học Sư phạm Tp.Hồ Chí Minh, Việt Nam

Main Article Content

Abstract

Let  be an arbitrary field. Denote by  the group of all infinite matrices of the form 

 

where  is an  matrix with determinant  for some positive integer , and  is an infinite upper triangular matrix with all diagonal entries equal to . In this paper, we prove that every matrix in  can be expressed as the product of at most four commutators. This result provides a solution to Problem 8 in Nguyen (2024).

Keywords

Commutator, Commutator matrix, Infinite matrix, Upper triangular matrix, Vershik–Kerov group

Article Details

References

Nguyen, T. T. H. (2024). A survey of lengths of linear groups with respect to certain generating sets. Communications of the Korean Mathematical Society, 39(2), 279-302. https://doi.org/10.4134/CKMS.c230058
Gustafson, W. H., Halmos, P. R., & Radjavi, H. (1976). Products of involutions. Linear Algebra and Its Applications, 13, 157-162.
Hou, X., Li, S., & Zheng, Q. (2017). Expressing infinite matrices over rings as products of involutions. Linear Algebra and Its Applications, 532, 257-265.
Hou, X. (2019). Decomposition of infinite matrices into products of commutators of involutions. Linear Algebra and Its Applications, 563, 231-239. https://doi.org/10.1016/j.laa.2018.11.001