Subgroups of the General Linear Group That Contain Elementary Subgroup Over a Rank 2 Commutative Ring Extension
- Authors: Hoi T.N.1, Nhat N.H.1
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Affiliations:
- University of Science, VNU-HCM
- Issue: Vol 234, No 2 (2018)
- Pages: 256-267
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/241842
- DOI: https://doi.org/10.1007/s10958-018-4001-z
- ID: 241842
Cite item
Abstract
Let R = \( \prod \limits_{i\in I}{F}_i \) be the direct product of fields, and let\( S=R\left[\sqrt{d}\right]=\prod \limits_{i\in I}{F}_i\left[\sqrt{d_i}\right] \) be a rank 2 extension of R. The subgroups of the general linear group GL(2n,R), n ≥ 3, that contain the elementary group E (n, S) are described. It is shown that for every such a subgroup H there exists a unique ideal A ⊴ R such that E (n, S)E(2n,R,A) ≤ H ≤ NGL(2n,R) (E (n, S)E(2n,R,A)).
About the authors
T. N. Hoi
University of Science, VNU-HCM
Author for correspondence.
Email: tnhoi@hcmus.edu.vn
Viet Nam, Ho Chi Minh City
N. H. T. Nhat
University of Science, VNU-HCM
Email: tnhoi@hcmus.edu.vn
Viet Nam, Ho Chi Minh City