On the sectional category of subgroup inclusions and Adamson cohomology theory

The sectional category of a subgroup inclusion $H\hookrightarrow G$ can be defined as the sectional category of the corresponding map between Eilenberg–MacLane spaces. We extend a characterization of topological complexity of aspherical spaces given by Farber, Grant, Lupton and Oprea to the context of sectional category of subgroup inclusions and investigate it by means of Adamson cohomology theory.