6533b7d1fe1ef96bd125cf47
RESEARCH PRODUCT
Highly transitive actions of groups acting on trees
Yves StalderSoyoung MoonPierre Fimasubject
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 TheoryMathematicsdescription
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 a closed, orientable surface of genus g>1 admits a faithful and highly transitive action.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-01-01 | Proceedings of the American Mathematical Society |