  We know that any element A of the group SO(3) can be represented as A = A1 A2
A1', where A1, A1' are elements of SO1(2)={A is an element of SO(3) | Ae1=e1},
and SO2(2)={A is an element of SO(3) | Ae2=e2} . This fact is known as Euler's
angle. When this situation, a matrix A is called the generator.
  In the present paper, we shall show firstly that the similar results hold for
the groups SU(3), and Sp(3).
  Secondly, we shall show that any element g of the simply connected compact
Lie group F4 (respectively. E6) can be represented g= g1 g2 g1', where g1, g1'
are elements of Spin1(9), g2 is an element of Spin2(9) (respectively g1, g1'
are elements of Spin1(10), g2 is an element of Spin2(10)), where Spink(9) = {g
is an element of F4 | g Ek = Ek} (respectively Spink(10) = {g is an element of
E6 | g Ek = Ek}.
  Lastly, we shall show that any element g of the simply connected compact Lie
group E7 can be represented as g = g1 g2 g1 ' g2 ' g1", where g1, g1', g1 " are
elements of Spin1(12), g2, g2' are elements of Spin2(12), where Spink(12) = {g
is an element of E7 | g K(k)= K(k) g, g M(k) = M(k) g}.
