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# Odd characterizations of almost simple groups - 3-local and character theoretic methods

Astill, Sarah (2010)
Ph.D. thesis, University of Birmingham.

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## Abstract

In this PhD thesis we discuss methods of recognizing finite groups by the structure of normalizers of certain 3-subgroups. We explain a method for characterizing groups using character theoretic and block theoretic methods and we use these methods to characterize Alt(9). Furthermore, we describe a particular hypothesis related to the 3-local structure of finite groups of local characteristic 3 and characterize two almost simple proper extensions of $$\Omega$$$$_8$$ (2) as examples of the local approach to group recognition. We also give a 3-local characterization of the sporadic simple group HN using local methods whilst applying a character theoretic result.

Type of Work: Ph.D. thesis. Parker, Christopher Colleges (2008 onwards) > College of Engineering & Physical Sciences School of Mathematics Mathematics, group theory, classification of finite simple groups QA Mathematics University of Birmingham 520
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