Exercise 6, § 2

We use the notation of no. 2 and let N_0 be the subgroup of N consisting of the matrices all of whose entries are equal to 0 or 1. Show that B ∩ N_0 = T ∩ N_0 = {1} and that the canonical map j from N_0 to W = N/T is an isomorphism. Put S_0 = j^{-1}(S). Show that (G, B, N_0, S_0) is a Tits system and that (G, B, N, S) is the associated saturated Tits system.