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

[摘要] 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.

[发布机构] University:University of Birmingham;Department:School of Mathematics

[关键词] Q Science;QA Mathematics