Commutative Algebra for Cohomology Rings of Virtual Duality Groups Original Research Article

Cohomology rings of finite groups have strong duality properties, as shown by[4]and [16]. We prove here that cohomology rings of virtual duality groups have a ring theoretic duality property, which combines the duality properties of finite groups with the cohomological duality of the subgroup of finite index. The formal behaviour of the local cohomology theorem is precisely analogous to that for a compact Lie group [6], except that the dimension appears to be negative.