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

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

Abstract

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.

Publications

10 25 50

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