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Infinitely generated free nilpotent groups: completeness of the automorphism groups

Published online by Cambridge University Press:  13 July 2009

VLADIMIR TOLSTYKH
VLADIMIR TOLSTYKH*
Affiliation:
Department of Mathematics, Yeditepe University, 34755 Kayɩşdağɩ, Istanbul, Turkey. e-mail: [email protected]
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Abstract

We transfer the results of Dyer, Formanek and Kassabov on the automorphism towers of finitely generated free nilpotent groups to infinitely generated free nilpotent groups. We prove that the automorphism groups of infinitely generated free nilpotent groups are complete. By combining the results of Dyer, Formanek and Kassabov with the results in this paper, one gets that the automorphism tower of any free nilpotent group terminates after finitely many steps.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 147 , Issue 3 , November 2009 , pp. 541 - 566
Copyright
Copyright © Cambridge Philosophical Society 2009

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References

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