Computing Resolutions Over Finite p-Groups

A uniform and constructive approach for the computation of resolutions and for (co)homology computations for any finite p-group is detailed. The resolutions we construct ([32]) are, as vector spaces, as small as the minimal resolution of IFp over the elementary abelian p-group of the same order as the group under study. Our implementations are based on the development of sophisticated algebraic data structures. Applications to calculating functional cocycles are given and the possibility of constructing interesting codes using such methods is presented.

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