  Let k be an algebraically closed field. Given an extension A : B of
finite-dimensional k- algebras, we establish criteria ensuring that the
representation-theoretic notion of polynomial growth is preserved under ascent
and descent. These results are then used to show that principal blocks of
finite group schemes of odd characteristic are of polynomial growth if and only
if they are Morita equivalent to trivial extensions of radical square zero tame
hereditary algebras. In that case, the blocks are of domestic representation
type and the underlying group schemes are closely related to binary polyhedral
group schemes.
