Products in negative cohomology

In this paper, we investigate negative degree elements of group cohomology and their products. We give a definition for arbitrary groups, which generalizes the definitions of Tate for finite groups and Farrell for groups of finite virtual cohomological dimension. We find that for finite groups, if we take coefficients in a field of characteristics p, very often all products between elements of negative degree vanish. In particular, this happens when the depth of the positive cohomology ring is greater than one. The latter is the case, for example, when a Sylow p-subgroup has a non-cyclic center.