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Fusion Systems On Finite Groups and Alperin's Theorem
KTH, School of Engineering Sciences (SCI).
2014 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

Let G be a group and P a Sylow p-subgroup of G. A fusion system of G on P, denoted by FP (G), is the category with objects; subgroups of P, and morphisms induced by conjugation in G. This thesis gives a brief introduction to the theory fusion systems.

Two classical theorems of Burnside and Frobenius are stated and proved. These theorems may be seen as a starting point of the theory of fusion systems, even though the axiomatic foundation is due to Puig in the early 1990's.

An abstract fusion system F on a p-group P is dened and the notion of a saturated fusion system is discussed. It turns out that the fusion system of any nite group is saturated, but the converse; that a saturated fusion system is realizable on a nite group, is not always true.

Two versions of Alperin's fusion theorem are stated and proved. The first one is the classical formulation of Alperin and the second one, due to Puig, a version stated in the language of fusion systems. The differences between these two are investigated.

The fusion system F of GL2 (3) on the Sylow 2-subgroup isomorphicto SD16 is determined and the subgroups generating F are found.

Place, publisher, year, edition, pages
2014. , 33 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-154554OAI: oai:DiVA.org:kth-154554DiVA: diva2:757660
Educational program
Master of Science in Engineering -Engineering Physics
Supervisors
Available from: 2014-10-23 Created: 2014-10-23 Last updated: 2014-10-23Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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Output format
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