On finite groups of p-local rank one and a conjecture of Robinson
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 a...
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University of Leicester
1999
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ndltd-bl.uk-oai-ethos.bl.uk-6966512018-04-04T03:31:52ZOn finite groups of p-local rank one and a conjecture of RobinsonEaton, Charles1999We 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 G2.512University of Leicesterhttp://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.696651http://hdl.handle.net/2381/30542Electronic Thesis or Dissertation |
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512 |
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512 Eaton, Charles On finite groups of p-local rank one and a conjecture of Robinson |
| description |
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. |
| author |
Eaton, Charles |
| author_facet |
Eaton, Charles |
| author_sort |
Eaton, Charles |
| title |
On finite groups of p-local rank one and a conjecture of Robinson |
| title_short |
On finite groups of p-local rank one and a conjecture of Robinson |
| title_full |
On finite groups of p-local rank one and a conjecture of Robinson |
| title_fullStr |
On finite groups of p-local rank one and a conjecture of Robinson |
| title_full_unstemmed |
On finite groups of p-local rank one and a conjecture of Robinson |
| title_sort |
on finite groups of p-local rank one and a conjecture of robinson |
| publisher |
University of Leicester |
| publishDate |
1999 |
| url |
http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.696651 |
| work_keys_str_mv |
AT eatoncharles onfinitegroupsofplocalrankoneandaconjectureofrobinson |
| _version_ |
1718619907539599360 |