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On finite groups of p-local rank one and a conjecture of Robinson

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posted on 15.12.2014, 10:40 by Charles. Eaton
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.;.

History

Date of award

01/01/1999

Author affiliation

Mathematics

Awarding institution

University of Leicester

Qualification level

Doctoral

Qualification name

PhD

Language

en

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