Automatically presented groups

  • Anna Erschler

    École Normale Supérieure, Paris, France


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.

Cite this article

Anna Erschler, Automatically presented groups. Groups Geom. Dyn. 1 (2007), no. 1, pp. 47–59

DOI 10.4171/GGD/3