The Local Structure Theorem, the non-characteristic 2 case

Chris Parker, Gernot Stroth

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Abstract

Let p be a prime, G a finite Kpgroup, 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 SLOp(L)≠1 and LNG(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 languageEnglish
Pages (from-to)465-513
JournalLondon Mathematical Society. Proceedings
Volume120
Issue number4
Early online date11 Sep 2019
DOIs
Publication statusPublished - 1 Apr 2020

Keywords

  • 20D05
  • 20D06
  • 20D08 (primary)

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