Answer to Question #18671 in Abstract Algebra for Melvin Henriksen

Question

Let G be a maximal unipotent subgroup of GLn(k) over a field k. If char(k) = 0, show that G is a torsionfree, nilpotent, and uniquely divisible group, and that it is the union of a family of subgroups Hi ∼ k such that Hi ∩ Hj = {1} for all i <> j.