  We prove a theorem that gives a sufficient condition for the full basic
automorphism group of a complete Cartan foliation to admit a unique
(finite-dimensional) Lie group structure in the category of Cartan foliations.
Emphasize that the transverse Cartan geometry may not be effective. Some
estimates of the dimension of this group depending on the transverse geometry
are found. Further, we investigate Cartan foliations covered by fibrations.
When the global holonomy group of that foliation is discrete, we obtain the
explicit new formula for determining its basic automorphism Lie group. Examples
of computing the full basic automorphism group of complete Cartan foliations
are constructed.
