Some finiteness conditions for automorphism groups

Abstract

Many authors have investigated the behaviour of the elements of finite order of a group G when finiteness conditions are imposed on the automorphism group Aut G of G . The first result was obtained in 1955 by Baer [ 1 ], who proved thata torsion group with finitely many automorphisms is finite. This theorem was generalized by Nagrebeckii in [ 6 ], where he proved that if the automorphism group Aut G is finite then the set of elements of finite order of G is a finite subgroup.