Parabolic Subgroups of Linear Groups and the Vershik-Kerov Group Over 𝔽2

Abstract

We give a full description of parabolic subgroups of GL n (𝔽2) and present their properties. We show that all such subgroups are determined by a net of ideals. Using this result we prove that analogous statement is true for the Vershik–Kerov group — the group consisting of infinite matrices having finite number of nonzero coefficients under the main diagonal.