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The equivalence of exotic and block-exotic fusion systems

Serwene, P. (2021). The equivalence of exotic and block-exotic fusion systems. (Unpublished Doctoral thesis, City, University of London)

Abstract

One of the main problems in the theory of fusion systems is whether a fusion system occurs as the fusion system of a finite p-group if and only if it occurs as the fusion system of a p-block of a finite group. It is conjectured that the answer is yes. We present reduction theorems for this problem, reducing it to blocks of quasisimple groups in certain cases. One of these reductions is applied to settle the conjecture for a family of fusion systems discovered by Parker and Semeraro. We state a stronger version of the conjecture for the class of generalised block fusion systems. We show that several key reduction results for block fusion systems carry over to generalised block fusion systems. Finally, we extend a result of Cabanes proving the conjecture for unipotent blocks of finite groups of Lie type to generalised block fusion systems.

Publication Type: Thesis (Doctoral)
Subjects: Q Science > QA Mathematics
Departments: Doctoral Theses
School of Mathematics, Computer Science & Engineering
School of Mathematics, Computer Science & Engineering > Mathematics
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