  We determine the length of composition series of projective modules of
G-transitive algebras with an Auslander-Reiten component of Euclidean tree
class. Furthermore we show that modules with certain length of composition
series are periodic. We apply these results to G-transitive blocks of the
Universal enveloping of restricted p-Lie algebras and prove that G-transitive
principal blocks only allow components with Euclidean tree class if p=2.
Finally we deduce conditions for a smash product of a local basic algebra with
a commutative semi-simple group algebra to have components with Euclidean tree
class, depending on the components of the Auslander-Reiten quiver of the basic
algebra. We also develop some properties of the bilinear form dim Hom_A(-,-)
for the representation ring G(A) of any finite-dimensional algebra A.
