On a Question about Generalized Congruence Subgroups

Abstract

Elementary net (carpet) σ = (σij) is called admissible (closed) if the elementary net (carpet) group E(σ) 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) σ = (σij) over a field K). An example of field K and the net σ = (σij) of order n over the field K are presented so that subgroup ⟨tij(σij), tji(σji)⟩ is not coincident with group E(σ) ∩ ⟨tij(K), tji(K)⟩.