  The notion of topological entropy is originally defined for a single action.
Later it was extended by Kieffer for arbitrary discrete amenable groups.
Recently Friedland defined topological entropy for any discrete group actions
amenable or not. Lind, Schmidt and Ward extended Yuzvinskii's addition formula
from single action to abelian group actions. A result of Ward and Zhang
suggests that such extension might be possible in the amenable case. In this
paper we prove that the addition formula can not be extended for groups of
finite type with nonzero Euler-characteristcs e.g. for free groups or surface
groups.
