Constructing endotrivial modules

A classification of endotrivial modules over p-groups was recently completed by the author and Jacques Thévenaz relying on generators for the group of endotrivial modules created by Alperin, Dade and others. In this paper we present a completely new construction of a set of generators using methods of group cohomology, some of which were developed in the classification. The new method has the advantage that all endotrivial modules can be constructed by the homological technique. In addition, the method applies to endotrivial modules over groups that are not p-groups.