Geodesic
Recognizability of finite groups by Suzuki group
Archivum mathematicum, Tome 55 (2019) no. 4, pp. 225-228 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Let $G$ be a finite group. The main supergraph $\mathcal{S}(G)$ is a graph with vertex set $G$ in which two vertices $x$ and $y$ are adjacent if and only if $o(x) \mid o(y)$ or $o(y)\mid o(x)$. In this paper, we will show that $G\cong Sz(q)$ if and only if $\mathcal{S}(G)\cong \mathcal{S}(Sz(q))$, where $q=2^{2m+1}\ge 8$.
Let $G$ be a finite group. The main supergraph $\mathcal{S}(G)$ is a graph with vertex set $G$ in which two vertices $x$ and $y$ are adjacent if and only if $o(x) \mid o(y)$ or $o(y)\mid o(x)$. In this paper, we will show that $G\cong Sz(q)$ if and only if $\mathcal{S}(G)\cong \mathcal{S}(Sz(q))$, where $q=2^{2m+1}\ge 8$.
DOI : 10.5817/AM2019-4-225
Classification : 05C25, 20D08
Keywords: main supergraph; Suzuki group 
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Asboei, Alireza Khalili; Amiri, Seyed Sadegh Salehi. Recognizability of finite groups by Suzuki group. Archivum mathematicum, Tome 55 (2019) no. 4, pp. 225-228. doi: 10.5817/AM2019-4-225

[1] Alavi, H., Daneshkhah, A., Parvizi, H.: Groups of the same type as Suzuki groups. Int. J. Group Theory 8 (1) (2019), 35–42. | MR

[2] Chen, G.Y.: On Frobenius and $2$-Frobenius group. J. Southwest China Normal Univ. 20 (1995), 485–487, in Chinese.

[3] Glauberman, G.: Factorizations in local subgroups of finite groups. Regional Conference Series in Mathematics, no. 33, American Mathematical Society, Providence, R.I., 1977. | MR

[4] Hamzeh, A., Ashrafi, A.R.: Automorphism groups of supergraphs of the power graph of a finite group. European J. Combin. 60 (2017), 82–88. | DOI | MR

[5] Iranmanesh, A., Parvizi, H., Tehranian, A.: Characterization of Suzuki group by NSE and order of group. Bull. Korean Math. Soc. 53 (3) (2016), 651–656. | DOI | MR

[6] Khalili, A., Salehi, S.S.: Some results on the main supergraph of finite groups. Accepted in Algebra Discrete Math.

[7] Khalili, A., Salehi, S.S.: Some alternating and symmetric groups and related graphs. Beitr. Algebra Geom. 59 (2018), 21–24. | DOI | MR

[8] Khalili, A., Salehi, S.S.: The small Ree group $^{2}G_{2}(3^{2n+1})$ and related graph. Comment. Math. Univ. Carolin. 59 (3) (2018), 271–276. | MR

[9] Mazurov, V.D., Khukhro, E.I.: Unsolved problems in group theory. The Kourovka Notebook, (English version), ArXiv e-prints, (18), January 2014. Available at | arXiv | MR

[10] Salehi, S.S., Khalili, A.: Recognition of $L_{2}(q)$ by the main supergraph. Accepted in Iran. J. Math. Sci. Inform.

[11] Shi, W.J.: A characterization of Suzuki’s simple groups. Proc. Amer. Math. Soc. 114 (3) (1992), 589–591. | DOI | MR

[12] Williams, J.S.: Prime graph components of finite groups. J. Algebra 69 (2) (1981), 487–513. | DOI | MR | Zbl

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