The Local Structure Theorem, the non-characteristic 2 case

Chris Parker; Gernot Stroth

doi:10.1112/plms.12291

The Local Structure Theorem, the non-characteristic 2 case

Chris Parker, Gernot Stroth

Mathematics

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

189 Downloads (Pure)

Abstract

Let p be a prime, G a finite K_p‐group, S a Sylow p‐subgroup of G and Q be a large subgroupof G in S. The aim of the Local Structure Theorem [Mem. Amer.Math. Soc. 242 (2016) 1147] is to provide structural information about subgroups L with S⩽L, O_p(L)≠1 and L≰N_G(Q).There is, however, one configuration where no structural informationabout L can be given using the methods in Meierfrankenfeld, Stellmacher and Stroth [Mem. Amer. Math. Soc. 242 (2016) 1147]. In this paperwe show that for p=2 this hypothetical configuration cannot occur. Weanticipate that our theorem will be used in the programme to revise theclassification of the finite simple groups.

Original language	English
Pages (from-to)	465-513
Journal	London Mathematical Society. Proceedings
Volume	120
Issue number	4
Early online date	11 Sept 2019
DOIs	https://doi.org/10.1112/plms.12291
Publication status	Published - 1 Apr 2020

Keywords

20D05
20D06
20D08 (primary)

Access to Document

10.1112/plms.12291Licence: None: All rights reserved

Parker_&_Stroth_The_Local_Structure_Theorem_the_non-characteristic_2_case_London_Mathematical_Society_Proceedings_2019
This is the accepted version of the following article: Parker, C & Stroth, G. (2020) 'The Local Structure Theorem, the non-characteristic 2 case', London Mathematical Society. Proceedings, vol. 120, no. 4, pp. 465-513, which has been published in final form at https://doi.org/10.1112/plms.12291
Accepted author manuscript, 569 KBLicence: Other (please specify with Rights Statement)

https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/plms.12291Licence: None: All rights reserved

Cite this

@article{ce711086def7497f96767e63b844829d,

title = "The Local Structure Theorem, the non-characteristic 2 case",

abstract = "Let p be a prime, G a finite Kp‐group, S a Sylow p‐subgroup of G and Q be a large subgroupof G in S. The aim of the Local Structure Theorem [Mem. Amer.Math. Soc. 242 (2016) 1147] is to provide structural information about subgroups L with S⩽L, Op(L)≠1 and L≰NG(Q).There is, however, one configuration where no structural informationabout L can be given using the methods in Meierfrankenfeld, Stellmacher and Stroth [Mem. Amer. Math. Soc. 242 (2016) 1147]. In this paperwe show that for p=2 this hypothetical configuration cannot occur. Weanticipate that our theorem will be used in the programme to revise theclassification of the finite simple groups.",

keywords = "20D05, 20D06, 20D08 (primary)",

author = "Chris Parker and Gernot Stroth",

year = "2020",

month = apr,

day = "1",

doi = "10.1112/plms.12291",

language = "English",

volume = "120",

pages = "465--513",

journal = "London Mathematical Society. Proceedings ",

issn = "0024-6115",

publisher = "London Mathematical Society",

number = "4",

}

TY - JOUR

T1 - The Local Structure Theorem, the non-characteristic 2 case

AU - Parker, Chris

AU - Stroth, Gernot

PY - 2020/4/1

Y1 - 2020/4/1

N2 - Let p be a prime, G a finite Kp‐group, S a Sylow p‐subgroup of G and Q be a large subgroupof G in S. The aim of the Local Structure Theorem [Mem. Amer.Math. Soc. 242 (2016) 1147] is to provide structural information about subgroups L with S⩽L, Op(L)≠1 and L≰NG(Q).There is, however, one configuration where no structural informationabout L can be given using the methods in Meierfrankenfeld, Stellmacher and Stroth [Mem. Amer. Math. Soc. 242 (2016) 1147]. In this paperwe show that for p=2 this hypothetical configuration cannot occur. Weanticipate that our theorem will be used in the programme to revise theclassification of the finite simple groups.

AB - Let p be a prime, G a finite Kp‐group, S a Sylow p‐subgroup of G and Q be a large subgroupof G in S. The aim of the Local Structure Theorem [Mem. Amer.Math. Soc. 242 (2016) 1147] is to provide structural information about subgroups L with S⩽L, Op(L)≠1 and L≰NG(Q).There is, however, one configuration where no structural informationabout L can be given using the methods in Meierfrankenfeld, Stellmacher and Stroth [Mem. Amer. Math. Soc. 242 (2016) 1147]. In this paperwe show that for p=2 this hypothetical configuration cannot occur. Weanticipate that our theorem will be used in the programme to revise theclassification of the finite simple groups.

KW - 20D05

KW - 20D06

KW - 20D08 (primary)

UR - http://www.scopus.com/inward/record.url?scp=85081038588&partnerID=8YFLogxK

U2 - 10.1112/plms.12291

DO - 10.1112/plms.12291

M3 - Article

SN - 0024-6115

VL - 120

SP - 465

EP - 513

JO - London Mathematical Society. Proceedings

JF - London Mathematical Society. Proceedings

IS - 4

ER -

The Local Structure Theorem, the non-characteristic 2 case

Abstract

Keywords

Access to Document

Fingerprint

Cite this