Group with periodic cohomology
This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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A group is said to have periodic cohomology if there exists a cohomology class for some positive integer , such that the cup product with defines an isomorphism between and for every . In particular, the sequence of cohomology groups is periodic.
A finite group with periodic cohomology is a finite group that has periodic cohomology.