Morris, Thomas Bembridge Slater (2011). Nilpotent injectors in finite groups. University of Birmingham. Ph.D.
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Morris11PhD.pdf
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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: | Thesis (Doctorates > Ph.D.) | ||||||
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Award Type: | Doctorates > Ph.D. | ||||||
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College/Faculty: | Colleges (2008 onwards) > College of Engineering & Physical Sciences | ||||||
School or Department: | School of Mathematics | ||||||
Funders: | Engineering and Physical Sciences Research Council | ||||||
Subjects: | Q Science > QA Mathematics | ||||||
URI: | http://etheses.bham.ac.uk/id/eprint/3066 |
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