The lifting problem in group cohomology

Abstract

The concept of lifting is well known from Schur's theory of projective representations of finite groups (Schur, 1904). In cohomological terms it means that for a given finite group G there is a central group extension E of G, a so-called lifting group of G, such that every 2-dimensional central cocycle class on G belongs to the kernel of the inflation map from G to E. The purpose of this paper is to extend this concept to higher-dimensional cocycles and to prove some results about the corresponding lifting groups.