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 second cohomology group) of $G$ on $A$, comprising those cohomology classes that can be represented by an 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