Tits alternatives for graph products
By Y. Antol'in, Ashot Minasyan. 2011
91 citations recorded by the source corpus.
We discuss various types of Tits Alternative for subgroups of graph products of groups, and prove that, under some natural conditions, a graph product of groups satisfies a given form of Tits Alternative if and only if each vertex group satisfies this alternative. As a corollary, we show that every finitely generated subgroup of a graph product of virtually solvable groups is either virtually solvable or large. As another corollary, we prove that every non-abelian subgroup of a right angled Artin group has an epimorphism onto the free group of rank 2. In the course of the paper we develop the theory of parabolic subgroups, which allows to describe the structure of subgroups of graph products that contain no non-abelian free subgroups. We also obtain a number of results regarding the stability of some group properties under taking graph products.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f1787e7811dd7a1bdac528216e03f5ec83b65e3e
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In Computational Theory and Mathematics
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Citations in the corpus
- Acylindrical hyperbolicity of groups acting on trees (2013, unknown): “NIS OSIN [39]. Further properties of graph products have been investigated in the works of Hermiller and Meier [45], Hsu and Wise [47], Januszkiewicz and ´Swia¸tkowski [52], and Antol´ın and Minasyan [2]. Recall that the link linkΓ(v), of a vertex v ∈ VΓ, is the set of all vertices of Γ that are adj”
- Automorphisms of graph products of groups from a geometric perspective (2018, background): “In particular, since satisfying the Tits alternative is a property stable under graph products [AM15] and under extensions, one can deduce from Corollary C a combination theorem for the Tits Alternative for such automorphism groups.”