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Thesis

Spectral properties of finite groups

Abstract:

This thesis concerns the diameter and spectral gap of finite groups. Our focus shall be on the asymptotic behaviour of these quantities for sequences of finite groups arising as quotients of a fixed infinite group.

In Chapter 3 we give new upper bounds for the diameters of finite groups which do not depend on a choice of generating set. Our method exploits the commutator structure of certain profinite groups, in a fashion analogous to the Solovay-Kitaev procedure from quantum comput...

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Role:
Supervisor
Type of award:
DPhil
Level of award:
Doctoral
Awarding institution:
University of Oxford

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