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).