Abstract:
The automorphism orbits of a group G is the orbits of Aut(G) acting on G. It is well-known that a finite group has exactly two automorphism orbits if and only if G is isomorphic to a finite dimensional space over a fintie field.
In this talk, we give a classification of finite groups with exactly three automorphism orbits. As an ``intermediate product'', we also prove a conjecture posed by Gross in 1976.
