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 $E(\sigma)\cap\langle t_{ij}(K), \ t_{ji}(K)\rangle$.
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