Search results for " 20B22"

showing 3 items of 3 documents

Highly transitive actions of groups acting on trees

2015

We show that a group acting on a non-trivial tree with finite edge stabilizers and icc vertex stabilizers admits a faithful and highly transitive action on an infinite countable set. This result is actually true for infinite vertex stabilizers and some more general, finite of infinite, edge stabilizers that we call highly core-free. We study the notion of highly core-free subgroups and give some examples. In the case of amalgamated free products over highly core-free subgroups and HNN extensions with highly core-free base groups we obtain a genericity result for faithful and highly transitive actions. In particular, we recover the result of D. Kitroser stating that the fundamental group of …

Vertex (graph theory)20B22 20E06 20E08Transitive relationApplied MathematicsGeneral Mathematics010102 general mathematicsamenable actionsHighly transitive actionsTransitive actionGroup Theory (math.GR)0102 computer and information sciences01 natural sciencesgroups acting on trees[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]CombinatoricsMathematics::Group TheoryFree product010201 computation theory & mathematicsFOS: MathematicsMSC: Primary 20B22; Secondary 20E06 20E08 43A07Countable setHNN extension0101 mathematicsMathematics - Group TheoryMathematicsProceedings of the American Mathematical Society
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Homogeneous actions on the random graph

2018

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.

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 graphMathematicsGroups, Geometry, and Dynamics
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Highly transitive actions of free products

2013

We characterize free products admitting a faithful and highly transitive action. In particular, we show that the group $\PSL_2(\Z)\simeq (\Z/2\Z)*(\Z/3\Z)$ admits a faithful and highly transitive action on a countable set.

Transitive actionHighly transitive actionsMSC: Primary: 20B22 20E06Group Theory (math.GR)01 natural sciencesBaire category Theorem[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]CombinatoricsFree products0103 physical sciencesFOS: MathematicsCountable set0101 mathematics20B22MathematicsTransitive relation20E06Group (mathematics)Mathematics::Operator Algebras010102 general mathematics20E06 20B2216. Peace & justiceFree productBaire category theorem010307 mathematical physicsGeometry and TopologyMathematics - Group Theory
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