We study
automorphism groups of trivial strongly minimal structures. First
we give a
characterization of structures of bounded valency
through their groups of
automorphisms.
Then we characterize the triplets of groups which can be
realized as the automorphism group of a non algebraic component,
the subgroup stabilizer of a point and
the subgroup of strong automorphisms in a trivial strongly minimal
structure, and also we give a reconstruction result.
Finally, using HNN extensions we show that any profinite group can be
realized as the stabilizer of a point in a strongly minimal structure of
bounded valency.