The principal results of this
paper are several characterizations of the class of artinian almost abelian groups.
Several corollaries of the main characterization are given, one of which states
that a torsion group G which has a finite group of automorphisms is finite,
and an abelian torsion group which has a countable automorphism group is
finite. In a concluding section, the class of artinian almost abelian groups
and the class of finite groups are characterized by formal group-theoretical
properties.