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Currently displaying 1 – 2 of 2

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Recognizability of finite groups by Suzuki group

Alireza Khalili Asboei; Seyed Sadegh Salehi Amiri — 2019

Archivum Mathematicum

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 $G ≅ S z (q)$ if and only if $𝒮 (G) ≅ 𝒮 (S z (q))$ , where $q = 2^{2 m + 1} \geq 8$ .

On the average number of Sylow subgroups in finite groups

Alireza Khalili Asboei; Seyed Sadegh Salehi Amiri — 2022

Czechoslovak Mathematical Journal

We prove that if the average number of Sylow subgroups of a finite group is less than $\frac{41}{5}$ and not equal to $\frac{29}{4}$ , then $G$ is solvable or $G / F (G) ≅ A_{5}$ . In particular, if the average number of Sylow subgroups of a finite group is $\frac{29}{4}$ , then $G / N ≅ A_{5}$ , where $N$ is the largest normal solvable subgroup of $G$ . This generalizes an earlier result by Moretó et al.

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