Free product of nontrivial groups is infinite

Statement
Suppose $$G$$ and $$H$$ are nontrivial groups (i.e., neither of them is a trivial group). Then, the fact about::external free product $$G * H$$ is infinite.

Related facts

 * Free product of nontrivial groups is centerless, which yields that central implies amalgam-characteristic
 * Free product of nontrivial groups has no nontrivial finite normal subgroup, which yields that finite normal implies amalgam-characteristic
 * Free product of nontrivial groups has no nontrivial periodic normal subgroup, which yields that periodic normal implies amalgam-characteristic