# Group cohomology of free nilpotent groups

From Groupprops

This article gives specific information, namely, group cohomology, about a family of groups, namely: free nilpotent group.

View group cohomology of group families | View other specific information about free nilpotent group

This article describes the group cohomology of the free nilpotent group of nilpotency class .

## Homology groups for trivial group action

FACTS TO CHECK AGAINST(homology group for trivial group action):

First homology group: first homology group for trivial group action equals tensor product with abelianization

Second homology group: formula for second homology group for trivial group action in terms of Schur multiplier and abelianization|Hopf's formula for Schur multiplier

General: universal coefficients theorem for group homology|homology group for trivial group action commutes with direct product in second coordinate|Kunneth formula for group homology

### Over the integers

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