Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Examples of finitely presented groups with strong fixed point properties and property (T)

Indira Chatterji, Martin Kassabov

Abstract

We construct a finitely presented group with property (T) which can not act on on reasonable spaces. Such group is constructed using an generalization of Hall embedding theorem, where property (T) is added at the expense of weakening the simplicity requirement.

Examples of finitely presented groups with strong fixed point properties and property (T)

Abstract

We construct a finitely presented group with property (T) which can not act on on reasonable spaces. Such group is constructed using an generalization of Hall embedding theorem, where property (T) is added at the expense of weakening the simplicity requirement.
Paper Structure (5 theorems, 1 equation)

This paper contains 5 theorems, 1 equation.

Key Result

Theorem 1

For any non-trivial element $g\in \mathrm{SL}_\infty(\mathbb{Z})$ there is an embedding of the group $\mathrm{SL}_\infty(\mathbb{Z})$ into a finitely presented property (T) group $\Gamma$ that is normally generated by $g$.

Theorems & Definitions (9)

  • Theorem 1
  • Corollary 2
  • Theorem 3
  • Lemma 4
  • Remark 5
  • proof : Proof of Lemma \ref{['ringembed']}
  • Lemma 6
  • proof
  • proof : Proof of Theorem \ref{['gengen']}