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Trudy Mat. Inst. Steklov., 1978, Volume 148, Pages 43–57 (Mi tm2497)  

This article is cited in 15 scientific papers (total in 15 papers)

Subgroups of the general linear group over a semilocal ring that contain a group of diagonal matrices

Z. I. Borevich, N. A. Vavilov


Full text: PDF file (1580 kB)

English version:
Proceedings of the Steklov Institute of Mathematics, 1980, 148, 41–54

Bibliographic databases:

UDC: 519.46

Citation: Z. I. Borevich, N. A. Vavilov, “Subgroups of the general linear group over a semilocal ring that contain a group of diagonal matrices”, Algebra, number theory and their applications, Trudy Mat. Inst. Steklov., 148, 1978, 43–57; Proc. Steklov Inst. Math., 148 (1980), 41–54

Citation in format AMSBIB
\Bibitem{BorVav78}
\by Z.~I.~Borevich, N.~A.~Vavilov
\paper Subgroups of the general linear group over a~semilocal ring that contain a~group of diagonal matrices
\inbook Algebra, number theory and their applications
\serial Trudy Mat. Inst. Steklov.
\yr 1978
\vol 148
\pages 43--57
\mathnet{http://mi.mathnet.ru/tm2497}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=558939}
\zmath{https://zbmath.org/?q=an:0444.20039|0453.20040}
\transl
\jour Proc. Steklov Inst. Math.
\yr 1980
\vol 148
\pages 41--54


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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. N. A. Vavilov, “On subgroups of the unitary group over a semilocal ring”, Russian Math. Surveys, 37:4 (1982), 145–146  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. I. Z. Golubchik, “On subgroups of the general linear group $GL_n(R)$ over an associative ring $R$”, Russian Math. Surveys, 39:1 (1984), 157–158  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. N. A. Vavilov, “Linear groups generated by one-parameter groups of one-dimensional transformations”, Russian Math. Surveys, 44:1 (1989), 265–266  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. E. V. Dybkova, “Naddiagonalnye podgruppy giperbolicheskoi unitarnoi gruppy dlya khoroshego formennogo koltsa nad polem”, Voprosy teorii predstavlenii algebr i grupp. 5, Zap. nauchn. sem. POMI, 236, POMI, SPb., 1997, 87–96  mathnet  mathscinet  zmath; E. V. Dybkova, “Overdiagonal subgroups of the hyperbolic unitary group for a good form ring over a field”, J. Math. Sci. (New York), 95:2 (1999), 2096–2101  crossref
    5. A. A. Panin, “Teoriya Galua dlya odnogo klassa polnykh dedekindovykh struktur”, Voprosy teorii predstavlenii algebr i grupp. 5, Zap. nauchn. sem. POMI, 236, POMI, SPb., 1997, 129–132  mathnet  mathscinet  zmath; A. A. Panin, “The Galois theory for a class of modular the complete lattices”, J. Math. Sci. (New York), 95:2 (1999), 2123–2125  crossref
    6. A. A. Panin, A. V. Yakovlev, “Teoriya Galua dlya odnogo klassa dedekindovykh struktur”, Voprosy teorii predstavlenii algebr i grupp. 5, Zap. nauchn. sem. POMI, 236, POMI, SPb., 1997, 133–148  mathnet  mathscinet  zmath; A. A. Panin, A. V. Yakovlev, “The Galois theory for a class of modular lattices”, J. Math. Sci. (New York), 95:2 (1999), 2126–2135  crossref
    7. E. V. Dybkova, “Teorema Borevicha dlya giperbolicheskoi unitarnoi gruppy nad nekommutativnym telom”, Voprosy teorii predstavlenii algebr i grupp. 12, Zap. nauchn. sem. POMI, 321, POMI, SPb., 2005, 136–167  mathnet  mathscinet  zmath; E. V. Dybkova, “The theorem of Borewich for the hyperbolic unitary group over a skew field”, J. Math. Sci. (N. Y.), 136:3 (2006), 3908–3925  crossref
    8. K. Yu. Lavrov, “Podgruppy ortogonalnykh grupp chetnogo poryadka nad lokalnym polem”, Voprosy teorii predstavlenii algebr i grupp. 12, Zap. nauchn. sem. POMI, 321, POMI, SPb., 2005, 240–250  mathnet  mathscinet  zmath; K. Yu. Lavrov, “Subgroups of the orthogonal groups of even degree over a local field”, J. Math. Sci. (N. Y.), 136:3 (2006), 3966–3971  crossref
    9. E. A. Sopkina, “Klassifikatsiya gruppovykh podskhem $\operatorname{GL}_n$, soderzhaschikh rasschepimyi maksimalnyi tor”, Voprosy teorii predstavlenii algebr i grupp. 12, Zap. nauchn. sem. POMI, 321, POMI, SPb., 2005, 281–296  mathnet  mathscinet  zmath; E. A. Sopkina, “Classitification of group subschemes in $\operatorname{GL}_n$, that contain a split maximal torus”, J. Math. Sci. (N. Y.), 136:3 (2006), 3988–3995  crossref
    10. E. V. Dybkova, “Nadgruppy diagonalnoi gruppy v giperbolicheskoi unitarnoi gruppe nad prostym artinovym koltsom. I”, Voprosy teorii predstavlenii algebr i grupp. 14, Zap. nauchn. sem. POMI, 338, POMI, SPb., 2006, 155–172  mathnet  mathscinet  zmath; E. V. Dybkova, “Overgroups of the diagonal group in the hyperbolic unitary group over a simple Artin ring”, J. Math. Sci. (N. Y.), 145:1 (2007), 4781–4789  crossref
    11. N. A. Vavilov, “O podgruppakh simplekticheskoi gruppy, soderzhaschikh subsystem subgroup”, Voprosy teorii predstavlenii algebr i grupp. 16, Zap. nauchn. sem. POMI, 349, POMI, SPb., 2007, 5–29  mathnet  mathscinet  elib; N. A. Vavilov, “On subgroups of symplectic group containing a subsystem subgroup”, J. Math. Sci. (N. Y.), 151:3 (2008), 2937–2948  crossref  elib
    12. N. A. Vavilov, “Subgroups of $\operatorname{SL}_n$ over a semilocal ring”, J. Math. Sci. (N. Y.), 147:5 (2007), 6995–7004  mathnet  crossref  mathscinet  elib  elib
    13. N. Vavilov, “Geometriya 1-torov v $\mathrm{GL}_n$”, Algebra i analiz, 19:3 (2007), 119–150  mathnet  mathscinet  zmath  elib; N. Vavilov, “Geometry of 1-tori in $\mathrm{GL}(n,T)$”, St. Petersburg Math. J., 19:3 (2008), 407–429  crossref  isi
    14. N. Vavilov, “Vesovye elementy grupp Shevalle”, Algebra i analiz, 20:1 (2008), 34–85  mathnet  mathscinet  zmath  elib; N. Vavilov, “Weight elements of Chevalley groups”, St. Petersburg Math. J., 20:1 (2009), 23–57  crossref  isi
    15. N. A. Dzhusoeva, V. A. Koibaev, “Normalizator elementarnoi setevoi gruppy, assotsiirovannoi s nerasschepimym torom, v polnoi lineinoi gruppe nad polem”, Voprosy teorii predstavlenii algebr i grupp. 26, Zap. nauchn. sem. POMI, 423, POMI, SPb., 2014, 105–112  mathnet  mathscinet; N. A. Dzhusoeva, V. A. Koibaev, “Normalizer of an elementary net group associated with a non-split torus in the general linear group over a field”, J. Math. Sci. (N. Y.), 209:4 (2015), 549–554  crossref
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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