Some results related to finiteness properties of groups for families of subgroups

@article{Puttkamer2018SomeRR,
  title={Some results related to finiteness properties of groups for families of subgroups},
  author={Timm von Puttkamer and Xiaolei Wu},
  journal={arXiv: Group Theory},
  year={2018}
}
For a group $G$ we consider the classifying space $E_{\mathcal{VC}yc}(G)$ for the family of virtually cyclic subgroups. We show that an Artin group admits a finite model for $E_{\mathcal{VC}yc}(G)$ if and only if it is virtually cyclic. This solves a conjecture of Juan-Pineda and Leary and a question of L\"uck-Reich-Rognes-Varisco for Artin groups. We then study the conjugacy growth of CAT(0) groups and show that if a CAT(0) group contains a free abelian group of rank two, its conjugacy growth… Expand