# Symmetric 2-cocycle for trivial group action

## Definition

Suppose is a group and is an abelian group. A function is termed a **symmetric 2-cocycle for trivial group action** if it satisfies the following conditions:

Condition name | Expression for condition |
---|---|

2-cocycle for a group action (particularly, 2-cocycle for trivial group action) | for all |

symmetric | for all |