A finiteness condition on automorphism groups
The automorphism \(\alpha\) of the group \({\mathcal G}\) is called ``virtually trivial'' if its group of fixed elements has finite index in \({\mathcal G}\). (Such automorphisms have also been called ``bounded'' automorphisms.) Groups with only virtually trivial automorphisms are here called VTA- groups. They are FC-groups (that is, groups with finite classes of conjugate elements), and are shown to be even FD-groups (that is, groups with finite derived groups). Moreover, the automorphism group of a VTA- group is locally finite; moreover the centre of the group is reduced and its primary components are all finite. If a VTA-group is periodic, then it has finite exponent and its centre is finite. Criteria for a group to be a VTA-group are given, as well as a number of interesting examples.
scientific article; zbMATH DE number 4038079