A seven-term exact sequence for the cohomology of a group extension. (Q1946101)

In this interesting paper, the authors construct a seven term exact sequence involving the low dimensional cohomology groups of a group extension. Their construction of connecting maps is purely group theoretic and is based on mostly well known interpretations of the low dimensional cohomology groups, such as derivations, semi-direct complements, extensions and crossed modules. Although the existence of such a sequence can be derived using spectral sequence arguments, there is little knowledge about some of the maps occurring in the sequence. The authors here give a complete and usable description of all the maps.