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

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.

Name dc:type.qualificationname

d_ph

Level dc:type.qualificationlevel

d_ph

Grantor dc:publisher.institution

University of Birmingham

Year dc:date.issued

2010

Author dc:creator

• Astill, Sarah

• QA Mathematics