Odd Characterizations of Almost Simple Groups (PhD Thesis 2009)

2012/09/25 by Sarah Astill, Astill, Sarah
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems #math.GR

paper · pdf · doi:10.48550/arxiv.1209.5542

arxiv created 2012/09/25 · openalex publication_date 2012/09/25 · arxiv updated 2012/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Ω⁺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.

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