Groups acting on the line with at most $2$ fixed points: an extension of Solodov's theorem
Group Theory
2022-10-17 v1 Dynamical Systems
Abstract
A classical result by Solodov states that if a group acts on the line such that any non-trivial element has at most one fixed point, then the action is either abelian or semi-conjugate to an affine action. We show that the same holds if we relax the assumption, requiring that any non-trivial element has at most 2 fixed points.
Cite
@article{arxiv.2210.07616,
title = {Groups acting on the line with at most $2$ fixed points: an extension of Solodov's theorem},
author = {João Carnevale},
journal= {arXiv preprint arXiv:2210.07616},
year = {2022}
}
Comments
7 pages