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The basic automorphism group ${A}_B(M,F)$ of a Cartan foliation $(M, F)$ isthe quotient group of the automorphism group of $(M, F)$ by the normalsubgroup, which preserves every leaf invariant. For Cartan foliations coveredby fibrations, we find sufficient conditions for the existence of a structureof a finite-dimensional Lie group in their basic automorphism groups. Estimatesof the dimension of these groups are obtained. For some class of Cartanfoliations with integrable an Ehresmann connection, a method for finding ofbasic automorphism groups is specified.

Basic automorphism of Cartan foliations covered by fibrations