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# Nilpotent injectors in finite groups

Morris, Thomas Bembridge Slater (2011)
Ph.D. thesis, University of Birmingham.

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## Abstract

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.

Type of Work: Ph.D. thesis. Flavell, Paul Colleges (2008 onwards) > College of Engineering & Physical Sciences School of Mathematics QA Mathematics University of Birmingham 3066
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