Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Saturated Fusion Systems
KTH, School of Engineering Sciences (SCI).
2014 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

A fusion system is a category on a nite p-group, P, which encodes "conjugacy" relations among the subgroups of P. In this thesis fusion systems of nite groups and ways to prove saturation of abstract fusion systems is investigated. First an introduction to fusion systems of nite groups and the notion of abstract fusion systems is given. Theorems of Burnside and Frobenius regarding fusion systems of nite groups are considered and proven. Alperins fusion theorem formulated for nite groups is considered and used in the proofs. It is proved that all fusion systems of nite groups are saturated.

An investigation in simpler ways of proving that a fusion system is saturated is done. First Alperins fusion theorem formulated for abstract fusion systems is considered which says that, a fusion system, denoted by F, is generated by the automorphism groups of some special subgroups.  Further investigation is done in how this set of special groups, that generates F, can be used to check if F is saturated. A theorem of Craven, though originally stated by Puig, is then considered and proven. The theorem says that is suffices to check that the conjugacy classes of, so called, F-centric subgroups are saturated in order to check that the fusion system F is saturated. Also a theorem of [5] is considered and proven. The theorem says that an even smaller set of conjugacy classes than the set of F-centric subgroups is needed to check saturation.

Section 1-2 are written together with Karl Amundsson and Eric Ahlqvist.

Place, publisher, year, edition, pages
2014. , 30 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-154556OAI: oai:DiVA.org:kth-154556DiVA: diva2:757682
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

Open Access in DiVA

Oliver Gäfvert kandidatexam(2320 kB)115 downloads
File information
File name FULLTEXT01.pdfFile size 2320 kBChecksum SHA-512
a75601aed3e83467b61f1e699522b796fa8287ed4aefff07b7da3750c3a4343e1027699d85e575ebe4b5dd99b66b486925ca772aba679230a6cf487f5bcf158b
Type fulltextMimetype application/pdf

By organisation
School of Engineering Sciences (SCI)
Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 115 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

urn-nbn

Altmetric score

urn-nbn
Total: 204 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf