JournalsggdVol. 1 , No. 1DOI 10.4171/ggd/3

Automatically presented groups

  • Anna Erschler

    École Normale Supérieure, Paris, France
Automatically presented groups cover


We introduce the notions of automatically presented groups and piecewise automatically presented groups. We show that if G is a piecewise automatically presented group satisfying the property T of Kazhdan, then G is finite. We prove that if G is amenable and finitely presented, then G is virtually abelian. We give further restrictions for a group to be piecewise automatically presented and study properties of such groups. We also give examples of automatically presented groups.