A. Galt

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math.GR2020

Minimal supplements in normalizers of maximal tori of $F_{4} (q)$

Alexey Galt, Alexey Staroletov

Let $G$ be a finite group of Lie type $F_{4}$ with the Weyl group $W$ . For every maximal torus $T$ of $G$ , we find the minimal order of a supplement to $T$ in its algebraic normalize…

math.GR2018

On splitting of the normalizer of a maximal torus in $E_{6} (q)$

Alexey Galt, Alexey Staroletov

Let $G$ be a finite group of Lie type $E_{6}$ over $F_{q}$ (adjoint or simply connected) and $W$ be the Weyl group of $G$ . We describe maximal tori $T$ such that $T$ has a complement i…

math.GR2018

On Shalev's conjecture for type $A_{n}$ and $^{2} A_{n}$

Alexey Galt, Amit Kulshrestha, Anupam Singh +1

In the paper we consider images of finite simple projective special linear and unitary groups under power words. In particular, we show that if $G\simeq \PSL_n^\varepsilon (q)$, th…

Minimal supplements in normalizers of maximal tori of F4​(q)

On splitting of the normalizer of a maximal torus in E6​(q)

On Shalev's conjecture for type An​ and 2An​

Minimal supplements in normalizers of maximal tori of $F_{4} (q)$

On splitting of the normalizer of a maximal torus in $E_{6} (q)$

On Shalev's conjecture for type $A_{n}$ and $^{2} A_{n}$