- Titel
- How local is the Local Structure Theorem for finite groups with a large p-subgroup?
- Zitierfähige Url:
- https://nbn-resolving.org/urn:nbn:de:bsz:14-qucosa2-949690
- Erstveröffentlichung
- 2025
- Datum der Einreichung
- 20.08.2024
- Datum der Verteidigung
- 09.12.2024
- Abstract (EN)
- In the Introduction of the Local Structure Theorem for finite groups with a large p-subgroup [MSS16] Meierfrankenfeld, Stellmacher and Stroth write: “It is obvious that one cannot get any information about M and its action on YM without discussing in one way or another the embedding of M into G. But a priori, it is not clear at all what type of embedding properties one should study and how they would help to get this information”. Here G is a finite group and M a cleverly chosen subgroup, with YM being a canonically determined elementary abelian, normal p-subgroup of M. On the one side, an answer to the question contained in the above citation is given by the result proven by Meierfrankenfeld, Stellmacher and Stroth; on the other side, one may ask how much of the group G is necessary for such result and how much is lost or changed by retaining only the plocal information of G, i.e. the information carried by the normalizers of non-trivial p-subgroups. In some way, which will hopefully become more clear and specific by the end of this Introduction, this dissertation can be seen as attempt to answer such question: we replace the group G with localities, as defined in 2.2.7, our choice of structures encoding precisely the p-local information of G, and look for an analogous of the Local Structure Theorem. In order to provide enough context to understand the statement and reach of [MSS16] as well as reasons and ideas behind the development of localities, we need a long historical digression and a detailed enough description of the strategy that was successful in proving the Local Structure Theorem. For the readers’ convenience we accordingly split our Introduction.
- Verweis
- The Local Structure Theorem for finite groups with a large p-subgroup
- Freie Schlagwörter (EN)
- Finite groups, fusion systems, localities, local group theory, large subgroups
- Klassifikation (DDC)
- 510
- Klassifikation (RVK)
- SK 260
- GutachterIn
- Prof. Dr. Ellen Henke
- Prof. Dr. Bernd Stellmacher
- Prof. Dr. Chris Parker
- BetreuerIn Hochschule / Universität
- Prof. Dr. Ellen Henke
- Den akademischen Grad verleihende / prüfende Institution
- Technische Universität Dresden, Dresden
- Version / Begutachtungsstatus
- publizierte Version / Verlagsversion
- URN Qucosa
- urn:nbn:de:bsz:14-qucosa2-949690
- Veröffentlichungsdatum Qucosa
- 30.01.2025
- Dokumenttyp
- Dissertation
- Sprache des Dokumentes
- Englisch
- Lizenz / Rechtehinweis
CC BY 4.0