|T |+‐resplendent models and the Lascar group

In this paper we show that in every |T |⁺‐resplendent model N , for every A ? N such that |A | ≤ |T |, the group Autf(N/A ) of strong automorphisms is the least very normal subgroup of the group Aut(N/A ) and the quotient Aut(N/A )/Autf(N/A ) is the Lascar group over A . Then we generalize this result to every |T |⁺‐saturated and strongly |T |⁺‐homogeneous model. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)