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 Mat. Sb., 1996, Volume 187, Number 2, Pages 19–36 (Mi msb107)

On subgroup of the special linear group of degree 2 over an infinite field

E. L. Bashkirov

Minsk Institute of Radio Technology

Abstract: We study the subgroups of $SL_2(K)$ over a field $K$ that comprise a conjugate in $GL_2(K)$ of the group of upper-unitriangular matrices of degree 2 over an infinite field $k$ such that $K/k$ is an algebraic extension.

DOI: https://doi.org/10.4213/sm107

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English version:
Sbornik: Mathematics, 1996, 187:2, 175–192

Bibliographic databases:

UDC: 512.743
MSC: 20G15

Citation: E. L. Bashkirov, “On subgroup of the special linear group of degree 2 over an infinite field”, Mat. Sb., 187:2 (1996), 19–36; Sb. Math., 187:2 (1996), 175–192

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Bashkirov, EL, “Linear groups over a skew field of quaternions containing the group T-n(A, Phi) over a subsfield”, Archiv der Mathematik, 79:5 (2002), 321
2. E. L. Bashkirov, “On subgroups of the general linear group over the skew field of quaternions which include the symplectic group”, Siberian Math. J., 44:2 (2003), 225–234
3. Bashkirov, EL, “Some completely reducible linear groups over a quaternion division ring containing a root subgroup”, Communications in Algebra, 31:12 (2003), 5727
4. Bashkirov, EL, “Irreducible linear groups of degree 3 over a quaternion division ring containing a root subgroup”, Communications in Algebra, 32:5 (2004), 1747
5. Bashkirov, EL, “Irreducible linear groups of degree four over a quaternion division algebra that contain a subgroup diag (T-3 (K, Phi(0)), 1)”, Journal of Algebra, 287:2 (2005), 319
6. Bashkirov, EL, “Transvection parameter sets in linear groups over associative division rings and special Jordan algebras defined by these rings”, Archiv der Mathematik, 87:4 (2006), 295
7. Bashkirov, EL, “Irreducible linear groups of degree four over a quaternion division algebra that contain a root subgroup”, Communications in Algebra, 34:6 (2006), 1931
8. N. Vavilov, “Geometry of 1-tori in $\mathrm{GL}(n,T)$”, St. Petersburg Math. J., 19:3 (2008), 407–429
9. Bashkirov, EL, “Linear groups over locally finite extensions of infinite fields”, International Journal of Algebra and Computation, 17:5–6 (2007), 905
10. Bashkirov, EL, “Completely reducible linear groups over a quaternion division algebra that contain a root subgroup”, Communications in Algebra, 35:3 (2007), 1019
11. Tsagereishvili, VS, “On the order of magnitude of Haar-Fourier coefficients”, Analysis Mathematica, 35:4 (2009), 301
12. Bashkirov E.L, “On subgroups of orthogonal groups of isotropic quadratic forms”, Journal of Pure and Applied Algebra, 214:7 (2010), 1049–1062
13. Evgenii L. Bashkirov, “Linear groups of degree four containing the subgroup”, Journal of Pure and Applied Algebra, 215:7 (2011), 1688
14. E.L.. Bashkirov, “Linear Groups of Degree 4 Over a Quaternion Division Ring that Contain the Special Unitary Group of a Skew-Hermitian Form with Maximal Witt Index”, Communications in Algebra, 42:2 (2014), 704
15. E. L. Bashkirov, C. K. Gupta, “Linear Groups Over Integral Extensions of Semilocal Commutative Rings”, Communications in Algebra, 42:10 (2014), 4149
16. E.L.. Bashkirov, “On subgroups of the group $GL7$ over a field that contain a Chevalley group of type $G2$ over a subfield”, Journal of Pure and Applied Algebra, 2014
17. Bashkirov E.L., Eser H., “On Linear Groups of Degree 2 Over a Finite Commutative Ring”, International Conference on Analysis and Applied Mathematics, AIP Conference Proceedings, 1611, eds. Ashyralyev A., Malkowsky E., Amer Inst Physics, 2014, 204–207
18. Bashkirov E.L., “On Linear Groups of Degree 2 Over a Noncommutative Division Algebra”, Commun. Algebr., 44:3 (2016), 1033–1054
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