The Local Structure Theorem, the non-characteristic 2 case

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The Local Structure Theorem, the non-characteristic 2 case. / Parker, Chris; Stroth, Gernot.

In: London Mathematical Society. Proceedings , Vol. 120, No. 4, 01.04.2020, p. 465-513.

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@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",

}

RIS

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)

U2 - 10.1112/plms.12291

DO - 10.1112/plms.12291

M3 - Article

VL - 120

SP - 465

EP - 513

JO - London Mathematical Society. Proceedings

JF - London Mathematical Society. Proceedings

SN - 0024-6115

IS - 4

ER -