ResolutionSmallGroup(G,k):: Group, Int --> FreeResolution
ResolutionSmallGroup(G,k):: FpGroup, Int --> FreeResolution

Inputs a small group G and an integer k \ge 1. It returns k+1 terms of a free ZG-resolution of \mathbb Z.

If G is a finitely presented group then up to degree $2$ the resolution coincides with cellular chain complex of the universal cover of the 2 complex associated to the presentation of G. Thus the boundaries of the generators in degree 3 provide a generating set for the module of identities of the presentation.

This function was written by Irina Kholodna.