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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Induced automorphisms of free metabelian groups


Author: Orin Chein
Journal: Proc. Amer. Math. Soc. 31 (1972), 1-9
MSC: Primary 20E05
DOI: https://doi.org/10.1090/S0002-9939-1972-0297846-2
MathSciNet review: 0297846
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Abstract: Let $ F$ and $ \phi $ respectively be the free group and the free metabelian group of rank $ q$. Let $ {\phi _n}$ be the $ n$th group of the lower central series of $ \phi $. We show that, for $ q > 3$ and for any positive integer $ n$, every automorphism of $ \phi /{\phi _n}$, which is induced by an automorphism of $ \phi $, is induced by an automorphism of $ F$. This reopens the question of whether every automorphism of $ \phi $ is induced by an automorphism of $ F$ if $ q > 3$.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0297846-2
Keywords: Free group, free metabelian group, IA automorphism, induced automorphism, lower central series, Bachmuth representation
Article copyright: © Copyright 1972 American Mathematical Society