IIP subgroup of second cohomology group for trivial group action

Definition
Suppose $$G$$ is a group and $$A$$ is an abelian group. The group that we call the IIP subgroup of second cohomology group for trivial group action is defined in the following equivalent ways:


 * 1) It is the subgroup of the second cohomology group for the trivial group action (see also defining ingredient::second cohomology group) of $$G$$ on $$A$$, comprising those cohomology classes that can be represented by an defining ingredient::IIP 2-cocycle for trivial group action.
 * 2) It is the quotient group of the group of IIP 2-cocycles for trivial group action by the group of IIP 2-coboundaries for trivial group action.

Related notions

 * Cyclicity-preserving subgroup of second cohomology group for trivial group action