Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-28T13:19:54.084Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)