A connected Lie group H is
said to be uniformly finitely generated by a given pair of one-parameter subgroups if
there exists a positive integer n such that every element of H can be written as a
finite product of length at most n of elements chosen alternately from the two
one-parameter subgroups. Define the order of generation of H as the least such n. It
is shown that the order of generation of the affine group is either 4 or 5 while its
connected Lie subgroups (with two exceptions) have order of generation equal to
their dimension.
