On $(2,3,7)$-generation of maximal parabolic subgroups. Special issue on group theory

Let R be a ring with 1 and En(R) be the subgroup of GLn(R) generated by the matrices I + reij, r ∈ R, i ≠ j. We prove that the subgroup Pn, n̄, of En+n̄(R) consisting of the matrices of shape (A0BĀ), where A ∈ En(R), Ā ∈ En̄,(R) and B ∈ Matn, n̄,Ä(R), is (2, 3, 7)-generated whenever R is finitely generated and n, n̄ are large enough.