  We present three examples of countable homogeneous structures (also called
Fraisse limits) whose automorphism groups are not universal, namely, fail to
contain isomorphic copies of all automorphism groups of their substructures.
Our first example is a particular case of a rather general construction on
Fraisse classes, which we call diversification, leading to automorphism groups
containing copies of all finite groups. Our second example is a special case of
another general construction on Fraisse classes, the mixed sums, leading to a
Fraisse class with all finite symmetric groups appearing as automorphism groups
and at the same time with a torsion-free automorphism group of its Fraisse
limit. Our last example is a Fraisse class of finite models with arbitrarily
large finite abelian automorphism groups, such that the automorphism group of
its Fraisse limit is again torsion-free.
