On Self-Normalising Sylow $2$-Subgroups in Type A

Amanda Schaeffer Fry; Jay Taylor

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arXiv · 1701.00272

On Self-Normalising Sylow $2$-Subgroups in Type A

Amanda Schaeffer Fry·Jay Taylor

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Abstract

Navarro has conjectured a necessary and sufficient condition for a finite group $G$ to have a self-normalising Sylow $2$-subgroup, which is given in terms of the ordinary irreducible characters of $G$. The first-named author has reduced the proof of this conjecture to showing that certain related statements hold when $G$ is quasisimple. In this article we show that these conditions are satisfied when $G/Z(G)$ is $\mathrm{PSL}_n(q)$, $\mathrm{PSU}_n(q)$, or a simple group of Lie type defined over a finite field of characteristic $2$.

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BibTeX RIS

Amanda Schaeffer Fry, Jay Taylor. 2017-01-01. On Self-Normalising Sylow $2$-Subgroups in Type A. https://arxiv.org/abs/1701.00272

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