Cohomology rings of finite groups have strong duality properties, as shown by Benson and Carlson [4] and Greenlees [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. (C) 1997 Academic Press. [References: 25]
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