Freely decomposable automorphism groups
This article is a contribution to the question: which groups are automorphism groups? The following interesting theorem is proved. If G is a group such that Aut G is the free product H*K of non-trivial subgroups H and K, then \(| H| =2=| K|\). On the other hand if \(| H| =2=| K|\), then H*K is infinite dihedral, and hence is isomorphic with its automorphism group. The main tool in the proof is the Kurosh-Subgroup Theorem.
scientific article; zbMATH DE number 4105223