Groups with few automorphism orbits

Abstract: Let $G$ be a group, and consider the natural action of the automorphism group of $G$ on $G$. The orbits of this action are called the automorphism orbits of $G$. In this talk, we will give an overview of known results concerning groups with finitely many automorphism orbits, including results where $G$ is assumed to have a concrete, small number of automorphism orbits, such as $G$. We will then speak in more detail about a result, achieved in collaboration with Stephen Glasby from UWA (Perth), which provides a full classification of the finite $2$-groups with exactly three automorphism orbits.

group theory

Audience: researchers in the topic

GOThIC - Ischia Online Group Theory Conference

Series comments: Please send a message to andrea.caranti@unitn.it to receive a link to the Zoom room where the conference (a series of talks, actually) takes place.