Geodesic
On a question about generalized congruence subgroups
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 1, pp. 66-69

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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
Mots-clés : transvection. 
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     author = {Vladimir A. Koibaev},
     title = {On a question about generalized congruence subgroups},
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Vladimir A. Koibaev. On a question about generalized congruence subgroups. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 1, pp. 66-69. http://geodesic.mathdoc.fr/item/JSFU_2018_11_1_a9/