on the fusion of elementary abelian subgroups of a finite p-group

Lead Research Organisation: Lancaster University
Department Name: Mathematics and Statistics


The student will investigate the action of fusion systems on the poset of noncyclic elementary abelian subgroups of a finite p-group. The motivation comes from the relevance of this poset in the description of the group of endotrivial modules of a finite group, and on the relevance of elementary abelian p-subgroups in group cohomology (cf. Benson, D. J.; Grodal, J.; Henke, E., Group cohomology and control of p-fusion, Invent. Math., 197, 491-507, (2014)).
The student will study the p-local conditions that make components of the poset fuse, primarily when the fusion system is that defined by a finite group on a Sylow p-subgroup. One expects that the fusions of isolated vertices depend on the presence of essential subgroups, but this information alone may not suffice.


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Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/T518037/1 30/09/2020 29/09/2025
2614232 Studentship EP/T518037/1 30/09/2021 29/09/2025 Ophelia Schaller