Artinian, almost abelian groups and their groups of automorphisms

Annemarie Schlette

Vol. 29 (1969), No. 2, 403–425

DOI: 10.2140/pjm.1969.29.403

Abstract

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.

Mathematical Subject Classification

Primary: 20.56

Milestones

Received: 12 June 1968

Published: 1 May 1969