(1) Unité de Mathématiques Pures et Appliquées, CNRS, Ecole Normale Supérieure de Lyon, 46, Allëe d'Italie, 69364 Lyon cedex 07, France
Abstract:
Let be a group generated by a finite set S. We give a sufficient
condition for to have Kazhdan's property (T). This condition is
easy to check and gives Kazhdan constants. We give examples of
groups to which this method applies. We prove that in some setting
generic presentations define groups which satisfy this condition and
thus have property (T). Moreover we prove that small changes in the
presentation of a group satisfying this condition do not change the
fact that the group has property (T).