$\textrm {Aut}(F)\to \textrm {Aut}(F/F”)$ is surjective for free group $F$ of rank $\geq 4$
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- by Seymour Bachmuth and Horace Y. Mochizuki PDF
- Trans. Amer. Math. Soc. 292 (1985), 81-101 Request permission
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 $3$.References
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Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 292 (1985), 81-101
- MSC: Primary 20E36; Secondary 20F28
- DOI: https://doi.org/10.1090/S0002-9947-1985-0805954-3
- MathSciNet review: 805954