Fusion systems on \(p\)-groups of sectional rank 3

[摘要] 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.

[发布机构] University:University of Birmingham;Department:School of Mathematics

[关键词] Q Science;QA Mathematics