Groups, Geometry, and Dynamics
Full-Text PDF (133 KB) | Table of Contents | GGD summary
Automatically presented groups
Anna Erschler (1)(1) Laboratoire de Mathématique d'Orsay, Université Paris-Sud, Bâtiment 425, 91405, ORSAY CEDEX, 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.
Keywords: Property T, amenability, polycyclic group, nilpotent group, Grigorchuk topology, Cayley topology, groups generated by finite state automata, word problem, Haagerup property