Abstract
According to the result by Dyer and Formanek [4], the automorphism group of a finitely generated free two-step nilpotent group is complete except in the case when this group is a one- or three-generator (the three-generator groups have automorphism tower of height 2). The purpose of this paper is to prove that the automorphism group of an infinitely generated free two-step nilpotent group is also complete. (Recall that a group G is said to be complete if G is centreless and every automorphism is inner.)The paper may be considered as a contribution to the study of automorphism towers of relatively free groups.
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