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Groups with 2-generated Sylow subgroups and their character tables

Alexander Moretó and Benjamin Sambale

Vol. 323 (2023), No. 2, 337–358
Abstract

Let G be a finite group with a Sylow p-subgroup P. We show that the character table of G determines whether P has maximal nilpotency class and whether P is a minimal nonabelian group. The latter result is obtained from a precise classification of the corresponding groups G in terms of their composition factors. For p-constrained groups G we prove further that the character table determines whether P can be generated by two elements.

Keywords
maximal class, minimal nonabelian, Sylow subgroup, fusion system, character table
Mathematical Subject Classification
Primary: 20C15, 20D20
Milestones
Received: 7 September 2022
Revised: 15 April 2023
Accepted: 26 April 2023
Published: 2 June 2023
Authors
Alexander Moretó
Departament de Matemátiques
Universitat de Valéncia
Spain
Benjamin Sambale
Institut für Algebra, Zahlentheorie und Diskrete Mathematik
Leibniz Universität Hannover
Germany

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