C * -simplicity of HNN extensions and groups acting on trees
نویسندگان
چکیده
منابع مشابه
On Groups which contain no HNN-Extensions
A group is called HNN-free if it has no subgroups that are nontrivial HNN-extensions. 23 We prove that finitely generated HNN-free implies virtually polycyclic for a large class of groups. We also consider finitely generated groups with no free subsemigroups of rank 2 25 and show that in many situations such groups are virtually nilpotent. Finally, as an application of our results, we determine...
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We study superstable groups acting on trees. We prove that an action of an ω-stable group on a simplicial tree is trivial. This shows that an HNN-extension or a nontrivial free product with amalgamation is not ωstable. It is also shown that if G is a superstable group acting nontrivially on a Λ-tree, where Λ = Z or Λ = R, and if G is either α-connected and Λ = Z, or if the action is irreducible...
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The most useful constructions in Combinatorial Group Theory are amalgamated free products and HNN-extensions, and they are the two basic examples in the theory of graphs of groups due to Bass and Serre (see [9]). We recall that given a group G and a subgroup H 6 G together with monomorphisms (respectively homomorphisms) ψ, φ : H −→ G, the group determined by the presentation 〈 G, t; t−1ψ(h)t = ...
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It is shown that the knapsack problem, which was introduced by Myasnikov et al. for arbitrary finitely generated groups, can be solved in NP for graph groups. This result even holds if the group elements are represented in a compressed form by SLPs, which generalizes the classical NP-completeness result of the integer knapsack problem. We also prove general transfer results: NP-membership of th...
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ژورنال
عنوان ژورنال: Annales de l'Institut Fourier
سال: 2021
ISSN: 1777-5310
DOI: 10.5802/aif.3378