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Matematicheskie Zametki, 1998, Volume 64, Issue 6, Pages 863–870
DOI: https://doi.org/10.4213/mzm1465 (Mi mzm1465) 		 
This article is cited in 3 scientific papers (total in 3 papers)

On a matrix representation of a free group

A. N. Zubkov

Omsk State Pedagogical University
Full-text PDF (189 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm1465
Abstract: An analog of the well-known Sanov representation of a free non-Abelian group by matrices of size ⩾3 is studied. Instead of transvections used in the Sanov representation, we use matrices with “filled” first (second, etc.) column, except for the intersection with the diagonal, and we have ones on the diagonal and zeros at the other places. The “filled” places are occupied by the same parameter k. It is proved that, for k⩾5, these matrices generate a free group.
Received: 31.07.1997
English version:
Mathematical Notes, 1998, Volume 64, Issue 6, Pages 745–752
DOI: https://doi.org/10.1007/BF02313032
Bibliographic databases:
UDC: 512
Language: Russian
Citation: A. N. Zubkov, “On a matrix representation of a free group”, Mat. Zametki, 64:6 (1998), 863–870; Math. Notes, 64:6 (1998), 745–752
Citation in format AMSBIB
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\paper On a matrix representation of a free group
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\jour Math. Notes
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\issue 6
\pages 745--752
\crossref{https://doi.org/10.1007/BF02313032}
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  • https://doi.org/10.4213/mzm1465
  • https://www.mathnet.ru/eng/mzm/v64/i6/p863
    • This publication is cited in the following 3 articles:
    1. Fabian R. Lux, Emil Prodan, “Spectral and Combinatorial Aspects of Cayley-Crystals”, Ann. Henri Poincaré, 2023  crossref
    2. A. I. Nekritsukhin, “Ob odnom matrichnom predstavlenii svobodnoi gruppy”, Chebyshevskii sb., 14:3 (2013), 88–91  mathnet
    3. A. I. Nekritsukhin, “Trekhmernoe matrichnoe predstavlenie svobodnoi gruppy”, Chebyshevskii sb., 11:3 (2010), 111–113  mathnet  zmath
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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    References:73
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