| Summary: | <p>This work is divided into three parts, all of which are concerned with the characterisation of certain families of classical groups as doubly transitive permutation groups satisfying certain extra hypotheses.</p> <p>The first part is purely expository. It culminates in the characterisation andndash; due to Marggraf andndash; of the affine groups over GF(2).</p> <p>The second part deals with a characterisation of certain collineation groups of protective spaces as Jordan groups which admit a Jordan set of prime power cardinality and which have extra restrictions on some Sylow subgroups.</p> <p>The third part consists of results obtained while attempting to establish that insoluble groups of prime degree p (andgt;7), whose Sylow p-subgroups have index 3 in their normalisers, are of the form PSL(3,q), for suitable prime powers q.</p>
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