Electronic Thesis and Dissertation Repository

Degree

Doctor of Philosophy

Program

Mathematics

Supervisor

Jan Minac

Abstract

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.


Included in

Algebra Commons

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