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Mathematics of the USSR-Izvestiya, 1981, Volume 16, Issue 3, Pages 573–601
DOI: https://doi.org/10.1070/IM1981v016n03ABEH001321 (Mi im1742) 		 
This article is cited in 32 scientific papers (total in 32 papers)

On arithmetic groups generated by reflections in Lobachevskii spaces

V. V. Nikulin
English version PDF (1591 kB) Citations (32)
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DOI: https://doi.org/10.1070/IM1981v016n03ABEH001321
Abstract: Using È.  B. Vinberg's arithmeticity criterion, the author defines the notion of the Galois lattice of a discrete arithmetic group generated by reflections in a Lobachevskii space.
The author proves finiteness of the set of such lattices and, as a corollary, finiteness of the set of maximal discrete arithmetic groups generated by reflections for fixed dimension of the Lobachevskii space and fixed degree of the ground field over $\mathbf Q$.
Bibliography: 19 titles.
Received: 12.11.1979
Revised: 11.12.1979
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1980, Volume 44, Issue 3, Pages 637–669
Bibliographic databases:
Document Type: Article
UDC: 519.46 + 511.4
MSC: Primary 20F32, 51F15; Secondary 52A25
Language: English
Original paper language: Russian
Citation: V. V. Nikulin, “On arithmetic groups generated by reflections in Lobachevskii spaces”, Izv. Akad. Nauk SSSR Ser. Mat., 44:3 (1980), 637–669; Math. USSR-Izv., 16:3 (1981), 573–601
Citation in format AMSBIB
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\transl
\jour Math. USSR-Izv.
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\crossref{https://doi.org/10.1070/IM1981v016n03ABEH001321}
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  • https://doi.org/10.1070/IM1981v016n03ABEH001321
  • https://www.mathnet.ru/eng/im/v44/i3/p637
    • This publication is cited in the following 32 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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    Abstract page:690
    Russian version PDF:214
    English version PDF:13
    References:63
    First page:1
     
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