Application of conformal transformation groups for construction of relativistic theories

The group C8 is shown to be a direct product of the Lorentz group by two commutative one-dimensional groups Csub(1Q) and Csub(1γ) corresponding to scale transformations. Expression for the generator induced by the group Csub(1γ) is found. Generalization of the group C8 to the group C16 = C15 x Csub(1γ) is carried out in which C8 forms a subgroup and C15 is a well-known group of Canningham and Baitman conformal transformations. A possibility of interpreting coordinate and time transformations for the group C8 in the framework of passive and active viewpoints is discussed