On homogeneous vector bundles and groups of diffeomorphism of compact homogeneous spaces

Let $M$ be a homogeneous space of a compact Lie group $K$. We denote by $D_0(M)$ the connected component of the identity in the group of all $C^\infty$-diffeomorphisms of $M$. In this paper it is proved that $D_0(M)$ and some of its closed subgroups are finitely-generated topological groups. It is also proved that the topological $K$-modules arising from the action of the group $K$ on the spaces of $C^k$-sections of homogeneous vector bundles over $M$ are noetherian.
Bibliography: 13 titles.