Nilpotent injectors in finite groups
We prove that the odd nilpotent injectors (a certain type of maximal nilpotent subgroup) f a minimal simple group are all conjugate, extending the result from soluble groups. We also prove conjugacy in GU(\_3\)(q) and SU(\_3\)(q). In a minimal counterexample to the onjecture that the odd nilpotent i...
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University of Birmingham
2011
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ndltd-bl.uk-oai-ethos.bl.uk-5425072019-04-03T06:42:02ZNilpotent injectors in finite groupsMorris, Thomas Bembridge Slater2011We prove that the odd nilpotent injectors (a certain type of maximal nilpotent subgroup) f a minimal simple group are all conjugate, extending the result from soluble groups. We also prove conjugacy in GU(\_3\)(q) and SU(\_3\)(q). In a minimal counterexample to the onjecture that the odd nilpotent injectors of an arbitrary ¯nite group are all conjugate we show that there must be a component, which cannot be of type A\(_n\) except possibly 3 ¢ A(\_6\) or 3 ¢ A(\_7\). Finally, we produce a partial result on minimal simple groups for a more general type of nilpotent injector.510QA MathematicsUniversity of Birminghamhttps://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.542507http://etheses.bham.ac.uk//id/eprint/3066/Electronic Thesis or Dissertation |
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NDLTD |
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NDLTD |
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510 QA Mathematics |
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510 QA Mathematics Morris, Thomas Bembridge Slater Nilpotent injectors in finite groups |
| description |
We prove that the odd nilpotent injectors (a certain type of maximal nilpotent subgroup) f a minimal simple group are all conjugate, extending the result from soluble groups. We also prove conjugacy in GU(\_3\)(q) and SU(\_3\)(q). In a minimal counterexample to the onjecture that the odd nilpotent injectors of an arbitrary ¯nite group are all conjugate we show that there must be a component, which cannot be of type A\(_n\) except possibly 3 ¢ A(\_6\) or 3 ¢ A(\_7\). Finally, we produce a partial result on minimal simple groups for a more general type of nilpotent injector. |
| author |
Morris, Thomas Bembridge Slater |
| author_facet |
Morris, Thomas Bembridge Slater |
| author_sort |
Morris, Thomas Bembridge Slater |
| title |
Nilpotent injectors in finite groups |
| title_short |
Nilpotent injectors in finite groups |
| title_full |
Nilpotent injectors in finite groups |
| title_fullStr |
Nilpotent injectors in finite groups |
| title_full_unstemmed |
Nilpotent injectors in finite groups |
| title_sort |
nilpotent injectors in finite groups |
| publisher |
University of Birmingham |
| publishDate |
2011 |
| url |
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.542507 |
| work_keys_str_mv |
AT morristhomasbembridgeslater nilpotentinjectorsinfinitegroups |
| _version_ |
1719014036062863360 |