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.

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