Nilpotent injectors in finite groups

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http://eprints.org/relation/isVersionOf http://etheses.bham.ac.uk/id/document/17086 http://eprints.org/relation/isVolatileVersionOf http://etheses.bham.ac.uk/id/document/17086 http://eprints.org/relation/isIndexCodesVersionOf http://etheses.bham.ac.uk/id/document/17086 archive 4031 disk0/00/00/30/66 2011-12-01 12:36:16 2019-01-23 09:55:27 2011-12-01 12:36:16 thesis show 0 Morris Thomas Bembridge Slater Flavell Paul University of Birmingham Nilpotent injectors in finite groups unpub QA 10col_ephy 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simple groups for a more general type of nilpotent injector. 2011-12 2011-07 graduation eng author unchecked This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder. public 122 University of Birmingham School of Mathematics d_ph FALSE epsrc 2011-12 graduation