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Title: On finite groups of p-local rank one and a conjecture of Robinson
Author: Eaton, Charles
Awarding Body: University of Leicester
Current Institution: University of Leicester
Date of Award: 1999
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We use the classification of finite simple groups to verify a conjecture of Robinson for finite groups G where G/Op(G) has trivial intersection Sylow p-subgroups. Groups of this type are said to have p-local rank one, and it is hoped that this invariant will eventually form the basis for inductive arguments, providing reductions for the conjecture, or even a proof using the results presented here as a base. A positive outcome for Robinson's conjecture would imply Alperin's weight conjecture. It is shown that in proving Robinson's conjecture it suffices to demonstrate only that it holds for finite groups in which Op(G) is both cyclic and central. Part of the proof of the former result is used to complete the verification of Dade's inductive conjecture for the Ree groups of type G2.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available