Doctor of Philosophy
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 exiting recent development. We do this by showing the explicit bijection between basic commutators and the irreducible polynomials over a certain finite field.
Combariza, German A., "Descending Central Series of Free Pro-p-Groups" (2010). Electronic Thesis and Dissertation Repository. 68.