# Fusion systems on $$p$$-groups of sectional rank 3

Grazian, Valentina (2017). Fusion systems on $$p$$-groups of sectional rank 3. University of Birmingham. Ph.D.

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## Abstract

In this thesis we study saturated fusion systems on $$p$$-groups having sectional rank 3, for $$p$$ odd. We obtain a complete classification of simple fusion systems on p-groups having sectional rank 3 for $$p$$ ≥ 5, exhibiting a new simple exotic fusion system on a 7-group of order 7$$^∧$$5. We introduce the notion of pearls, defined as essential subgroups isomorphic to the groups C$$_p$$ X $$_p$$ and $$p$$$$_+$$$$^1$$$$^+$$$$^2$$ (for odd), and we illustrate some properties of fusion systems involving pearls. As for $$p$$ = 3, we determine the isomorphism type of a certain section of the 3-groups considered.

Type of Work: Thesis (Doctorates > Ph.D.)
Award Type: Doctorates > Ph.D.
Supervisor(s):
Supervisor(s)EmailORCID
Parker, ChristopherUNSPECIFIEDUNSPECIFIED
Licence:
College/Faculty: Colleges (2008 onwards) > College of Engineering & Physical Sciences
School or Department: School of Mathematics
Funders: Engineering and Physical Sciences Research Council, Other
Other Funders: The University of Birmingham
Subjects: Q Science > QA Mathematics
URI: http://etheses.bham.ac.uk/id/eprint/7670

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