Borge, I. C. (2001) A cohomological approach to the classification of groups. PhD thesis, University of Oxford.

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Abstract
In this thesis we apply methods from homological algebra to the study of finite groups. Let be a finite group and let be the field of elements. We consider the cohomology groups and and the Massey product structure on these cohomology groups, which we use to deduce properties about .
We tie the classical theory of Massey products in with a general method from deformation theory for constructing hulls of functors and see how far the strictly defined Massey products can take us in this setting.
We show how these Massey products relate to extensions of modules and to relations, giving us cohomological presentations of groups. These presentations will be minimal pro presentations and will often be different from the presentations we are used to.
This enables us to shed some new light on the classification of groups, in particular we give a `tree construction' illustrating how we can `produce' groups using cohomological methods. We investigate groups of exponent and some of the families of groups appearing in the tree. We also investigate the limits of these methods.
As an explicit example illustrating the theory we have introduced, we calculate Massey products using the Yoneda cocomplex and give 0deficiency presentations for split metacyclic groups using strictly defined Massey products.
We also apply these methods to the modular isomorphism problem, i.e. the problem whether (the isomorphism class of) is determined by . We give a new class of finite groups which can be distinguished using .
Item Type:  Thesis (PhD) 

Subjects:  A  C > Algebraic geometry 
Research Groups:  Algebra Research Group 
ID Code:  40 
Deposited By:  Eprints Administrator 
Deposited On:  10 Mar 2004 
Last Modified:  29 May 2015 18:15 
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