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J. Sib. Fed. Univ. Math. Phys., 2018, Volume 11, Issue 1, Pages 66–69 (Mi jsfu594)  

This article is cited in 1 scientific paper (total in 1 paper)

On a question about generalized congruence subgroups

Vladimir A. Koibaevab

a Southern Mathematical Institute VSC RAS, Markus, 22, Vladikavkaz, 362027
b North-Ossetian State University, Vatutin, 44-46, Vladikavkaz, 362025

Abstract: Elementary net (carpet) $\sigma=(\sigma_{ij})$ is called admissible (closed) if the elementary net (carpet) group $E(\sigma)$ does not contain a new elementary transvections. This work is related to the problem proposed by Y. N. Nuzhin in connection with the problem 15.46 from the Kourovka notebook proposed by V. M. Levchuk (admissibility (closure) of the elementary net (carpet) $\sigma = (\sigma_{ij})$ over a field $K$). An example of field $K$ and the net $\sigma=(\sigma_{ij})$ of order $n$ over the field $K$ are presented so that subgroup $\langle t_{ij}(\sigma_{ij}), t_{ji}(\sigma_{ji})\rangle$ is not coincident with group $E(\sigma)\cap\langle t_{ij}(K), t_{ji}(K)\rangle$.

Keywords: Carpets, carpet groups, nets, elementary nets, allowable elementary nets, closed elementary nets, elementary net group, transvection.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation
The work was supported by the Ministry of Education and Science of the Russian Federation and by Southern Institute of Mathematics (Vladikavkaz Scientific Centre of Russian Academy of Sciences).


DOI: https://doi.org/10.17516/1997-1397-2018-11-1-66-69

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UDC: 512.5
Received: 17.04.2017
Received in revised form: 20.05.2017
Accepted: 22.10.2017
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Citation: Vladimir A. Koibaev, “On a question about generalized congruence subgroups”, J. Sib. Fed. Univ. Math. Phys., 11:1 (2018), 66–69

Citation in format AMSBIB
\Bibitem{Koi18}
\by Vladimir~A.~Koibaev
\paper On a question about generalized congruence subgroups
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2018
\vol 11
\issue 1
\pages 66--69
\mathnet{http://mi.mathnet.ru/jsfu594}
\crossref{https://doi.org/10.17516/1997-1397-2018-11-1-66-69}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000431379500010}


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    This publication is cited in the following articles:
    1. V. A. Koibaev, “On a question about generalized congruence subgroups. I”, J. Math. Sci. (N. Y.), 243:4 (2019), 573–576  mathnet  crossref
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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