Groups Acting on Dendrons
- Authors: Malyutin A.V.1
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Affiliations:
- St.Petersburg Department of Steklov Mathematical Institute
- Issue: Vol 212, No 5 (2016)
- Pages: 558-565
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/237080
- DOI: https://doi.org/10.1007/s10958-016-2688-2
- ID: 237080
Cite item
Abstract
A dendron is defined as a continuum (a nonempty, connected, compact Hausdorff space) in which every two distinct points have a separation point. It is proved that if a group G acts on a dendron D by homeomorphisms, then either D contains a G-invariant subset consisting of one or two points or G contains a free noncommutative subgroup and, furthermore, the action is strongly proximal.
About the authors
A. V. Malyutin
St.Petersburg Department of Steklov Mathematical Institute
Author for correspondence.
Email: malyutin@pdmi.ras.ru
Russian Federation, St.Petersburg