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Free two-step nilpotent groups whose automorphism group is complete

Published online by Cambridge University Press:  26 October 2001

VLADIMIR TOLSTYKH
VLADIMIR TOLSTYKH
Affiliation:
Department of Mathematics, Kemerovo State University, Kemerovo, Russia
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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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 131 , Issue 1 , July 2001 , pp. 73 - 90
Copyright
2001 Cambridge Philosophical Society

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