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arXiv · 2205.13167

Groups with 2-generated Sylow subgroups and their character tables

Alexander Moretó·Benjamin Sambale
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Abstract

Let G be a finite group with 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 non-abelian 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.

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Alexander Moretó, Benjamin Sambale. 2022-05-26. Groups with 2-generated Sylow subgroups and their character tables. https://doi.org/10.2140/pjm.2023.323.337

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