An Automorphism of A Free Metabelian Group Without Fixed Points

Details An Automorphism of A Free Metabelian Group Without Fixed Points An Automorphism of A Free Metabelian Group Without Fixed Points

2003-11-26

arxiv.org/abs/math/0311490v1

Mathematics

Group Theory

5 pages

Scientific paper

We construct an example of an IA-automorphism of the free metabelian group of
rank $n\geq 3$ without nontrivial fixed points. That gives a negative answer to
the question raised by Shpilrain. By a result of Bachmuth \cite{Ba1}, such an
automorphism does not exist if the rank is equal to 2.

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