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 $E(\sigma)\cap\langle t_{ij}(K), \ t_{ji}(K)\rangle$.
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).
Received: 17.04.2017 Received in revised form: 20.05.2017 Accepted: 22.10.2017
Bibliographic databases:
Document Type:
Article
UDC:
512.5
Language: English
Citation:
Vladimir A. Koibaev, “On a question about generalized congruence subgroups”, J. Sib. Fed. Univ. Math. Phys., 11:1 (2018), 66–69