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Currently displaying 1 – 2 of 2

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A characterization of symplectic groups related to Fermat primes

Behnam Ebrahimzadeh; Alireza K. Asboei — 2021

Commentationes Mathematicae Universitatis Carolinae

We proved that the symplectic groups $PSp (4, 2^{n})$ , where $2^{2 n} + 1$ is a Fermat prime number is uniquely determined by its order, the first largest element orders and the second largest element orders.

The small Ree group $^{2} G_{2} (3^{2 n + 1})$ and related graph

Alireza K. Asboei; Seyed S. S. Amiri — 2018

Commentationes Mathematicae Universitatis Carolinae

Let $G$ be a finite group. The main supergraph $𝒮 (G)$ is a graph with vertex set $G$ in which two vertices $x$ and $y$ are adjacent if and only if $o (x) ∣ o (y)$ or $o (y) ∣ o (x)$ . In this paper, we will show that $G ≅^{2} G_{2} (3^{2 n + 1})$ if and only if $𝒮 (G) ≅ 𝒮 (^{2} G_{2} (3^{2 n + 1}))$ . As a main consequence of our result we conclude that Thompson’s problem is true for the small Ree group $^{2} G_{2} (3^{2 n + 1})$ .

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