6533b7d7fe1ef96bd126799f
RESEARCH PRODUCT
Homogeneous actions on the random graph
Pierre FimaSoyoung MoonYves Staldersubject
Random graphFinite group20B22 (primary) 20E06 20E05 05C63 54E52 (secondary)Group Theory (math.GR)Homogeneous actions16. Peace & justicegroups acting on trees[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]Action (physics)CombinatoricsMathematics::Group TheoryFree productHomogeneousBaire category theoremFOS: MathematicsDiscrete Mathematics and CombinatoricsCountable setBaire category theoremfree groupsGeometry and TopologyFinitely-generated abelian groupMathematics - Group TheoryMSC: 20B22 (primary); 20E06 20E05 05C63 54E52 (secondary)random graphMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-04-26 | Groups, Geometry, and Dynamics |