 ##  [Geometric Group Theory](/index.php/geometric-group-theory) 

  ##  [Geometric Group Theory](https://puremath.quantumdictionary.io/geometric-group-theory-0) 

  
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- Mathematics &amp; Logic -

**Pure Mathematics Dictionary**

 
Definition

A field that studies finitely generated groups via their actions on metric and topological spaces and via coarse geometric objects (Cayley graphs, quasi-isometries), using large-scale invariants to relate algebraic properties to geometric and dynamical behavior.