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Descending Central Series Of Free Pro-P-Groups, German A. Combariza
Descending Central Series Of Free Pro-P-Groups, German A. Combariza
Electronic Thesis and Dissertation Repository
In this thesis, we study the first three cohomology groups of the quotients of the descending central series of a free pro-p-group. We analyse the Lyndon-Hochschild- Serre spectral sequence up to degree three and develop what we believe is a new technique to compute the third cohomology group. Using Fox-Calculus we express the cocycles of a finite p-group G with coefficients on a certain module M as the kernel of a matrix composed by the derivatives of the relations of a minimal presentation for G. We also show a relation between free groups and finite fields, this is a new …