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On the basis-conjugating automorphism groups of free groups and free metabelian groups

Published online by Cambridge University Press:  08 December 2014

TAKAO SATOH
TAKAO SATOH*
Affiliation:
Department of Mathematics, Faculty of Science Division II, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku, Tokyo, 162-8601, Japan. e-mail: takao@rs.tus.ac.jp
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Abstract

In this paper we study the images of the Johnson homomorphisms of the basis-conjugating automorphism groups of free groups and free metabelian groups. In particular, we show that the Johnson image is contained in a certain proper Lie subalgebra $\mathfrak{p}$Mn of the derivation algebra of the Chen Lie algebra. Furthermore, we completely determine the Johnson images, and give the abelianisation of $\mathfrak{p}$Mn as a Lie algebra by using Morita's trace maps.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 158 , Issue 1 , January 2015 , pp. 83 - 109
Copyright
Copyright © Cambridge Philosophical Society 2014 

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