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

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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)

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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
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The Local Structure Theorem, the non-characteristic 2 case

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