On the intersection of tame subgroups in groups acting on trees

Konstantinos Lentzos; Mihalis Sykiotis

On the intersection of tame subgroups in groups acting on trees

Group Theory 2018-01-11 v3

Authors: Konstantinos Lentzos , Mihalis Sykiotis

Abstract

Let $G$ be a group acting on a tree $T$ with finite edge stabilizers of bounded order. We provide, in some very interesting cases, upper bounds for the complexity of the intersection $H\cap K$ of two tame subgroups $H$ and $K$ of $G$ in terms of the complexities of $H$ and $K$ . In particular, we obtain bounds for the Kurosh rank $Kr(H\cap K)$ of the intersection in terms of Kurosh ranks $Kr(H)$ and $Kr(K)$ , in the case where $H$ and $K$ act freely on the edges of $T$ .

Keywords

tame subgroup group acting on trees Kurosh rank subgroup intersection edge stabilizer

Cite

@article{arxiv.1703.01117,
  title  = {On the intersection of tame subgroups in groups acting on trees},
  author = {Konstantinos Lentzos and Mihalis Sykiotis},
  journal= {arXiv preprint arXiv:1703.01117},
  year   = {2018}
}

Comments

15 pages. v2 updated to mention recent work by other researchers. Minor changes. v3 revised version following the referee's comments. Statement of Theorem 3.3 corrected

On the intersection of tame subgroups in groups acting on trees

Abstract

Keywords

Cite

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