Abstract
By giving a constructive proof of Conjecture P of Newman and O’Brien, we reduce the classification of certain p-groups of coclass r to a finite calculation. For the case p=2 we show that all 2-groups of coclass r can be classified by finitely many parametrised presentations. A non-constructive proof of Conjecture P was given by du Sautoy, using the theory of zeta functions. Our constructive proof uses homological algebra. It yields more precise results and detailed structure theorems for the p-groups under consideration.
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