Originally Posted by
Turloughmack 1.Show that a free product of finite group is hyperbolic.
Here it must be a free finite product of finite groups, otherwise we end with a non-fin. gen. group which can't then
be hyperbolic.
Now we can use the fact that finite groups are (trivially) hyperbolic groups and thus a finite product, either free or cartesian, of
them is hyperbolic, too.
2. Let G, H be finitely generated groups with growth series g(z) and h(z) and generating sets X and Y. Then show that the growth series for [G x H] with respect to the disjoint union of X and Y is g(z).h(z).