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dc.contributor.advisorQuick, M. R. (Martyn R.)
dc.contributor.authorMcDougall-Bagnall, Jonathan M.
dc.description.abstractIt can be deduced from the Burnside Basis Theorem that if G is a finite p-group with d(G)=r then given any generating set A for G there exists a subset of A of size r that generates G. We have denoted this property B. A group is said to have the basis property if all subgroups have property B. This thesis is a study into the nature of these two properties. Note all groups are finite unless stated otherwise. We begin this thesis by providing examples of groups with and without property B and several results on the structure of groups with property B, showing that under certain conditions property B is inherited by quotients. This culminates with a result which shows that groups with property B that can be expressed as direct products are exactly those arising from the Burnside Basis Theorem. We also seek to create a class of groups which have property B. We provide a method for constructing groups with property B and trivial Frattini subgroup using finite fields. We then classify all groups G where the quotient of G by the Frattini subgroup is isomorphic to this construction. We finally note that groups arising from this construction do not in general have the basis property. Finally we look at groups with the basis property. We prove that groups with the basis property are soluble and consist only of elements of prime-power order. We then exploit the classification of all such groups by Higman to provide a complete classification of groups with the basis property.en_US
dc.publisherUniversity of St Andrews
dc.subjectGroup theoryen_US
dc.subjectGenerating setsen_US
dc.subjectFinite groupsen_US
dc.subjectBasis propertyen_US
dc.subjectFrattini subgroupen_US
dc.subject.lcshFinite groupsen_US
dc.subject.lcshFrattini subgroupsen_US
dc.titleGeneration problems for finite groupsen_US
dc.type.qualificationnamePhD Doctor of Philosophyen_US
dc.publisher.institutionThe University of St Andrewsen_US

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