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

This article is cited in 18 scientific papers (total in 18 papers)

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

Full text: PDF file (294 kB)
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 512.743
MSC: 20G15
Received: 14.04.1992

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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\paper On subgroup of the~special linear group of degree~2 over an~infinite field
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    Citing articles on Google Scholar: Russian citations, English citations
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    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  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    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  mathnet  crossref  mathscinet  zmath  isi
    3. Bashkirov, EL, “Some completely reducible linear groups over a quaternion division ring containing a root subgroup”, Communications in Algebra, 31:12 (2003), 5727  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    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  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    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  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    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  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    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  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    8. N. Vavilov, “Geometry of 1-tori in $\mathrm{GL}(n,T)$”, St. Petersburg Math. J., 19:3 (2008), 407–429  mathnet  crossref  mathscinet  zmath  isi  elib
    9. Bashkirov, EL, “Linear groups over locally finite extensions of infinite fields”, International Journal of Algebra and Computation, 17:5–6 (2007), 905  crossref  mathscinet  zmath  isi
    10. Bashkirov, EL, “Completely reducible linear groups over a quaternion division algebra that contain a root subgroup”, Communications in Algebra, 35:3 (2007), 1019  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    11. Tsagereishvili, VS, “On the order of magnitude of Haar-Fourier coefficients”, Analysis Mathematica, 35:4 (2009), 301  crossref  mathscinet  zmath  isi
    12. Bashkirov E.L, “On subgroups of orthogonal groups of isotropic quadratic forms”, Journal of Pure and Applied Algebra, 214:7 (2010), 1049–1062  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    13. Evgenii L. Bashkirov, “Linear groups of degree four containing the subgroup”, Journal of Pure and Applied Algebra, 215:7 (2011), 1688  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    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  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    15. E. L. Bashkirov, C. K. Gupta, “Linear Groups Over Integral Extensions of Semilocal Commutative Rings”, Communications in Algebra, 42:10 (2014), 4149  crossref  mathscinet  zmath  scopus  scopus  scopus
    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  crossref  mathscinet  scopus  scopus  scopus
    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  crossref  isi  scopus  scopus  scopus
    18. Bashkirov E.L., “On Linear Groups of Degree 2 Over a Noncommutative Division Algebra”, Commun. Algebr., 44:3 (2016), 1033–1054  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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