Minimal fusion systems with a unique maximal parabolic

Ellen Henke

doi:10.1016/j.jalgebra.2010.11.006

Minimal fusion systems with a unique maximal parabolic

Ellen Henke^* (Corresponding Author)

^*Corresponding author for this work

Mathematical Science

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

We define minimal fusion systems in a way that every non-solvable fusion system has a section which is minimal. Minimal fusion systems can also be seen as analogs of Thompsonʼs N-groups. In this paper, we consider a minimal fusion system FF on a finite p-group S that has a unique maximal p -local subsystem containing NF(S)NF(S). For an arbitrary prime p, we determine the structure of a certain (explicitly described) p -local subsystem of FF. If p=2p=2, this leads to a complete classification of the fusion system FF.

Original language	English
Pages (from-to)	318-367
Number of pages	50
Journal	Journal of Algebra
Volume	333
Issue number	1
Early online date	3 Dec 2010
DOIs	https://doi.org/10.1016/j.jalgebra.2010.11.006
Publication status	Published - 1 May 2011

Keywords

saturated fusion systems
group theory

Access to Document

10.1016/j.jalgebra.2010.11.006Licence: Unspecified

http://arxiv.org/abs/1007.2159

Cite this

@article{a6bdae1cd1304c9da37dd0befff3d2b7,

title = "Minimal fusion systems with a unique maximal parabolic",

abstract = "We define minimal fusion systems in a way that every non-solvable fusion system has a section which is minimal. Minimal fusion systems can also be seen as analogs of Thompsonʼs N-groups. In this paper, we consider a minimal fusion system FF on a finite p-group S that has a unique maximal p -local subsystem containing NF(S)NF(S). For an arbitrary prime p, we determine the structure of a certain (explicitly described) p -local subsystem of FF. If p=2p=2, this leads to a complete classification of the fusion system FF.",

keywords = "saturated fusion systems, group theory",

author = "Ellen Henke",

year = "2011",

month = may,

day = "1",

doi = "10.1016/j.jalgebra.2010.11.006",

language = "English",

volume = "333",

pages = "318--367",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - Minimal fusion systems with a unique maximal parabolic

AU - Henke, Ellen

PY - 2011/5/1

Y1 - 2011/5/1

N2 - We define minimal fusion systems in a way that every non-solvable fusion system has a section which is minimal. Minimal fusion systems can also be seen as analogs of Thompsonʼs N-groups. In this paper, we consider a minimal fusion system FF on a finite p-group S that has a unique maximal p -local subsystem containing NF(S)NF(S). For an arbitrary prime p, we determine the structure of a certain (explicitly described) p -local subsystem of FF. If p=2p=2, this leads to a complete classification of the fusion system FF.

AB - We define minimal fusion systems in a way that every non-solvable fusion system has a section which is minimal. Minimal fusion systems can also be seen as analogs of Thompsonʼs N-groups. In this paper, we consider a minimal fusion system FF on a finite p-group S that has a unique maximal p -local subsystem containing NF(S)NF(S). For an arbitrary prime p, we determine the structure of a certain (explicitly described) p -local subsystem of FF. If p=2p=2, this leads to a complete classification of the fusion system FF.

KW - saturated fusion systems

KW - group theory

U2 - 10.1016/j.jalgebra.2010.11.006

DO - 10.1016/j.jalgebra.2010.11.006

M3 - Article

SN - 0021-8693

VL - 333

SP - 318

EP - 367

JO - Journal of Algebra

JF - Journal of Algebra

IS - 1

ER -

Minimal fusion systems with a unique maximal parabolic

Abstract

Keywords

Access to Document

Fingerprint

Cite this