Sylow intersections and control of fusion

Let G be a finite group and let P be a Sylow p -subgroup of G . We prove that if the automizer of each intersection of two distinct Sylow p -subgroups is a p -group, then N G ( P ) controls strong G -fusion in P . In fact, more general results will be discussed in this note.

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Bibliographische Detailangaben
Veröffentlicht in:	Monatshefte für Mathematik 2023-08, Vol.201 (4), p.1197-1201
Hauptverfasser:	Meng, Hangyang, Tian, Jinyue, Guo, Xiuyun
Format:	Artikel
Sprache:	eng
Schlagworte:	Group theory Mathematics Mathematics and Statistics Subgroups
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Beschreibung
Zusammenfassung:	Let G be a finite group and let P be a Sylow p -subgroup of G . We prove that if the automizer of each intersection of two distinct Sylow p -subgroups is a p -group, then N G ( P ) controls strong G -fusion in P . In fact, more general results will be discussed in this note.
ISSN:	0026-9255 1436-5081
DOI:	10.1007/s00605-022-01731-z