Groups, Geometry, and Dynamics
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Automatically presented groupsAnna Erschler (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
Erschler A. Automatically presented groups. Groups Geom. Dyn. 1 (2007), 47-59. doi: 10.4171/GGD/3