Geodesic
Automatically presented groups
Anna Erschler1
1École Normale Supérieure, Paris, France
Groups, geometry, and dynamics, Tome 1 (2007) no. 1, pp. 47-59

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DOI

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.
DOI : 10.4171/ggd/3
Classification : 20-XX, 00-XX
Mots-clés : Property <span style="font-style: italic;">T</span>, amenability, polycyclic group, nilpotent group, Grigorchuk topology, Cayley topology, groups generated by finite state automata, word problem, Haagerup property

Anna Erschler  1

1 École Normale Supérieure, Paris, France 
Anna Erschler. Automatically presented groups. Groups, geometry, and dynamics, Tome 1 (2007) no. 1, pp. 47-59. doi: 10.4171/ggd/3
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