Applications of versal deformations to Galois theory

In this paper we study which solutions to an embedding problem can be constructed using a versal deformation of a group representation over an algebraically closed field of positive characteristic. This question reduces (at least stably) to finding which representations of finite groups have faithful versal deformations. We determine exactly when a versal deformation of a representation of a finite group is faithful in case the representation belongs to a cyclic block and its endomorphisms are given by scalar multiplications. Received: January 30, 2001