Local group theory, the amalgam method, and fusion systems

van Beek, Martin ORCID: 0000-0003-1465-0242 (2022). Local group theory, the amalgam method, and fusion systems. University of Birmingham. Ph.D.

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Abstract

In this thesis, we provide a framework in which certain configurations in saturated fusion systems can be characterized via the amalgam method. Along the way, we identify several rank 2 amalgams involving strongly $p$ -embedded subgroups, and recognize some finite simple groups as associated completions. In addition, as an application, we determine all saturated fusion systems supported on a Sylow
$p$ -subgroup of G $_2(p^n$ ) and PSU $_4(p^n$ ) for all primes $p$ and $n \in \mathbb{N}$ .