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YCor
YCor
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The following is a question asked to me these days by Gülin Ercan. --

Let $G = L(q^f)$ be a finite simple group of Lie type, and let $L(q) \cong H < G$$L(q) \cong H \le G$ be the group of fixed points of the automorphisms of $G$ induced by field automorphisms. In case $H$ is nonsolvable --, can there exist a nontrivial subgroup $N$ of $G$ which is normalized by $H$ and which has trivial intersection with $H$?

The following is a question asked to me these days by Gülin Ercan. --

Let $G = L(q^f)$ be a finite simple group of Lie type, and let $L(q) \cong H < G$ be the group of fixed points of the automorphisms of $G$ induced by field automorphisms. In case $H$ is nonsolvable -- can there exist a nontrivial subgroup $N$ of $G$ which is normalized by $H$ and which has trivial intersection with $H$?

The following is a question asked to me these days by Gülin Ercan.

Let $G = L(q^f)$ be a finite simple group of Lie type, and let $L(q) \cong H \le G$ be the group of fixed points of the automorphisms of $G$ induced by field automorphisms. In case $H$ is nonsolvable, can there exist a nontrivial subgroup $N$ of $G$ which is normalized by $H$ and which has trivial intersection with $H$?

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Stefan Kohl ♦
Stefan Kohl ♦
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Subgroups of finite simple groups $L(q^f)$ of Lie type normalized by $L(q)$

The following is a question asked to me these days by Gülin Ercan. --

Let $G = L(q^f)$ be a finite simple group of Lie type, and let $L(q) \cong H < G$ be the group of fixed points of the automorphisms of $G$ induced by field automorphisms. In case $H$ is nonsolvable -- can there exist a nontrivial subgroup $N$ of $G$ which is normalized by $H$ and which has trivial intersection with $H$?