An Automorphism of A Free Metabelian Group Without Fixed Points

Martin Kassabov

An Automorphism of A Free Metabelian Group Without Fixed Points

Group Theory 2007-05-23 v1

Authors: Martin Kassabov

Abstract

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.

Keywords

free metabelian group IA-automorphism fixed points rank Shpilrain's question

Cite

@article{arxiv.math/0311490,
  title  = {An Automorphism of A Free Metabelian Group Without Fixed Points},
  author = {Martin Kassabov},
  journal= {arXiv preprint arXiv:math/0311490},
  year   = {2007}
}

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5 pages

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