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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.
Received: 17.04.2017 Received in revised form: 20.05.2017 Accepted: 22.10.2017
Citation:
Vladimir A. Koibaev, “On a question about generalized congruence subgroups”, J. Sib. Fed. Univ. Math. Phys., 11:1 (2018), 66–69
Linking options:
https://www.mathnet.ru/eng/jsfu594 https://www.mathnet.ru/eng/jsfu/v11/i1/p66
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