Back to Search
Start Over
Homogeneous actions on the random graph
- Source :
- Groups, Geometry, and Dynamics, Groups, Geometry, and Dynamics, European Mathematical Society, 2021, 15 (1), pp.1-34. ⟨10.4171/GGD/589⟩, Groups, Geometry, and Dynamics, 2021, 15 (1), pp.1-34. ⟨10.4171/GGD/589⟩
- Publication Year :
- 2020
- Publisher :
- European Mathematical Society - EMS - Publishing House GmbH, 2020.
-
Abstract
- We show that any free product of two countable groups, one of them being infinite, admits a faithful and homogeneous action on the Random Graph. We also show that a large class of HNN extensions or free products, amalgamated over a finite group, admit such an action and we extend our results to groups acting on trees. Finally, we show the ubiquity of finitely generated free dense subgroups of the automorphism group of the Random Graph whose action on it have all orbits infinite.<br />Comment: Last author version sent to the journal. Includes corrections made during the review process
- Subjects :
- Random graph
Finite group
20B22 (primary), 20E06, 20E05, 05C63, 54E52 (secondary)
Group Theory (math.GR)
Homogeneous actions
16. Peace & justice
groups acting on trees
[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]
Action (physics)
Combinatorics
Mathematics::Group Theory
Free product
Homogeneous
Baire category theorem
FOS: Mathematics
Discrete Mathematics and Combinatorics
Countable set
free groups
Geometry and Topology
Finitely-generated abelian group
Mathematics - Group Theory
MSC: 20B22 (primary)
20E06, 20E05, 05C63, 54E52 (secondary)
random graph
Mathematics
Subjects
Details
- ISSN :
- 16617207 and 16617215
- Volume :
- 15
- Database :
- OpenAIRE
- Journal :
- Groups, Geometry, and Dynamics
- Accession number :
- edsair.doi.dedup.....00b71493f550ab4304d455d822efcdf5