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. 47–59DOI 10.4171/GGD/3