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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

$ {\rm Aut}(F)\to{\rm Aut}(F/F'')$ is surjective for free group $ F$ of rank $ \geq 4$


Authors: Seymour Bachmuth and Horace Y. Mochizuki
Journal: Trans. Amer. Math. Soc. 292 (1985), 81-101
MSC: Primary 20E36; Secondary 20F28
MathSciNet review: 805954
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Abstract: In this article, it is shown that the group of automorphisms of the free metabelian group $ \Phi (n)$ of rank $ n \geqslant 4$ is not only finitely generated but in fact every automorphism of $ \Phi (n)$ is induced by an automorphism of the free group of the same rank $ n$. This contrasts sharply with the authors' earlier result [4] that any set of generators of the group of automorphisms of the free metabelian group $ \Phi (3)$ of rank $ 3$ contains infinitely many automorphisms which are not induced by an automorphism of the free group of rank $ 3$.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0805954-3
PII: S 0002-9947(1985)0805954-3
Article copyright: © Copyright 1985 American Mathematical Society