Siberian Federal University

Elementary net (carpet) σ = ( σij) is called closed (admissible) if the elementary net (carpet) group E(σ ) does not contain a new elementary transvections. The work is related to the question of V. M. Levchuk 15.46 from the Kourovka notebook( closedness (admissibility) of the elementary net (carpet)over a field). Let R be a discrete valuation ring, K be the field of fractions of R, σ = (σ ij) be an elementary net of order n over R, ω = (ωij) be a derivative net for , and ωij is ideals of the ring R. It is proved that if K is a field of odd characteristic, then for the closedness (admissibility) of the net , the closedness (admissibility) of each pair (σ ij ; σ ji) is sufficient for all i ̸= j.