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Perturbation theory and free resolutions for nilpotent groups of class 2. (English) Zbl 0696.55024

This is the first of several papers on the cohomology of solvable groups. The author uses homological perturbation theory to construct a small (not necessarily minimal) free resolution for any nilpotent group G of class 2. The resolution reflects the structure of G as a central extension of an abelian group by an abelian group and is small enough so that the requisite calculations can actually be carried out.
Reviewer: T.W.Hungerford

MSC:

55R40 Homology of classifying spaces and characteristic classes in algebraic topology
20J06 Cohomology of groups
18G10 Resolutions; derived functors (category-theoretic aspects)
20F18 Nilpotent groups
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