Weak Tits alternative for groups acting geometrically on buildings

Chris Karpinski; Damian Osajda; Piotr Przytycki

Weak Tits alternative for groups acting geometrically on buildings

Group Theory 2024-06-12 v2

Authors: Chris Karpinski , Damian Osajda , Piotr Przytycki

Abstract

We show that if a group $G$ acts geometrically by type-preserving automorphisms on a building, then $G$ satisfies the weak Tits alternative, namely, that $G$ is either virtually abelian or contains a non-abelian free group.

Keywords

group actions algebraic group actions abelian groups

Cite

@article{arxiv.2306.16546,
  title  = {Weak Tits alternative for groups acting geometrically on buildings},
  author = {Chris Karpinski and Damian Osajda and Piotr Przytycki},
  journal= {arXiv preprint arXiv:2306.16546},
  year   = {2024}
}

Comments

16 pages, 5 figures. Published in press in Journal of Algebra at https://doi.org/10.1016/j.jalgebra.2024.05.015

Weak Tits alternative for groups acting geometrically on buildings

Abstract

Keywords

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