# IIP subgroup of second cohomology group for trivial group action

From Groupprops

## Definition

Suppose is a group and 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:

- It is the subgroup of the second cohomology group for the trivial group action (see also second cohomology group) of on , comprising those cohomology classes that can be represented by an IIP 2-cocycle for trivial group action.
- 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.