Which groups arise as Aut(A^2)?
by
Keith A. Kearnes
University of Colorado

Every group arises as the automorphism group of some algebra, which can be taken to be finite if the group is finite. Every group with an involution arises as the automorphism group of the square of some algebra, but some finite groups with involution do not arise as the automorphism group of the square of a finite algebra (e.g., the 4-element cyclic group). We will explain why a finite group G with central involution s arises as the automorphism group of the square of a finite algebra, with s representing the automorphism that switches the factors, if and only if G has a retraction onto {1, s}.

Date received: May 12, 2004