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Zapiski Nauchnykh Seminarov POMI, 2000, Volume 272, Pages 177–185 (Mi znsl1368)  
This article is cited in 1 scientific paper (total in 1 paper)

A conjugacy theorem for subgroups of $\mathrm{SL}_n$ containing the group of diagonal matrices

A. E. Egorov, A. A. Panin

Saint-Petersburg State University
Full-text PDF (170 kB) Citations (1)
Abstract: Let $R$ be a commutative local ring. It is proved that if $n\ge3$ and the residue field of $R$ contains at least $3n+2$ elements, then the subgroup of diagonal matrices in the special linear group of degree $n$ over $R$ is pronormal. For semilocal rings with the same restrictions on residue fields this subgroup is paranormal.
Received: 04.07.2000
English version:
Journal of Mathematical Sciences (New York), 2003, Volume 116, Issue 1, Pages 2982–2986
DOI: https://doi.org/10.1023/A:1023402826581
Bibliographic databases:
UDC: 519.46
Language: Russian
Citation: A. E. Egorov, A. A. Panin, “A conjugacy theorem for subgroups of $\mathrm{SL}_n$ containing the group of diagonal matrices”, Problems in the theory of representations of algebras and groups. Part 7, Zap. Nauchn. Sem. POMI, 272, POMI, St. Petersburg, 2000, 177–185; J. Math. Sci. (N. Y.), 116:1 (2003), 2982–2986
Citation in format AMSBIB
\Bibitem{EgoPan00}
\by A.~E.~Egorov, A.~A.~Panin
\paper A conjugacy theorem for subgroups of $\mathrm{SL}_n$ containing the group of diagonal matrices
\inbook Problems in the theory of representations of algebras and groups. Part~7
\serial Zap. Nauchn. Sem. POMI
\yr 2000
\vol 272
\pages 177--185
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1368}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1811798}
\zmath{https://zbmath.org/?q=an:1069.20038}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2003
\vol 116
\issue 1
\pages 2982--2986
\crossref{https://doi.org/10.1023/A:1023402826581}
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  • https://www.mathnet.ru/eng/znsl/v272/p177
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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