# Article

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Keywords:
element order; prime graph; Suzuki group
Summary:
One of the important questions that remains after the classification of the finite simple groups is how to recognize a simple group via specific properties. For example, authors have been able to use graphs associated to element orders and to number of elements with specific orders to determine simple groups up to isomorphism. In this paper, we prove that Suzuki groups $Sz(q)$, where $q\pm \sqrt{2q}+1$ is a prime number can be uniquely determined by the order of group and the number of elements with the same order.
References:
[1] Chen, G.Y.: About Frobenius groups and $2$-Frobenius groups. J. Southwest China Normal Univ. 20 (5) (1995), 485–487.
[2] Ebrahimzadeh, B., Iranmanesh, A., Parvizi Mosaed, H.: A new characterization of Ree group $^2G_2 (q)$ by the order of group and number of elements with same order. Int. J. Group Theory 6 (4) (2017), 1–6. MR 3695074
[3] Frobenius, G.: Verallgemeinerung des Sylowschen Satze. Berliner Sitz (1895), 981–983.
[4] Gorenstein, D.: Finite Groups. Harper and Row, New York, 1980. MR 0569209 | Zbl 0463.20012
[5] Khalili Asboei, A., Amiri, S.S., Iranmanesh, A., Tehranian, A.: A new characterization of sporadic simple groups by NSE and order. J. Algebra Appl. 12 (2) (2013), 1250158. DOI 10.1142/S0219498812501587 | MR 3005607
[6] Khalili Asboei, A., Iranmanesh, A.: Characterization of the linear groups $L_2(p)$. Czechoslovak Math. J. 64 (139) (2014), no. 459–464. MR 3277747
[7] Parvizi Mosaed, H., Iranmanesh, A., Tehranian, A.: Characterization of suzuki group by nse and order of group. Bull. Korean Math. Soc. 53 (3) (2016), 651–656. DOI 10.4134/BKMS.b140564 | MR 3508660
[8] Shao, C.G., Shi, W., Jiang, Q.H.: Characterization of simple $K_4$-groups. Front Math. China 3 (3) (2008), 355–370. DOI 10.1007/s11464-008-0025-x | MR 2425160 | Zbl 1165.20020
[9] Suzuki, M.: On a class of doubly transitive groups. Ann. of Math. 2 (75) (1962), 105–145. DOI 10.2307/1970423 | MR 0136646
[10] Wiliams, J.S.: Prime graph components of finite groups. J. Algebra 69 (2) (1981), 487–512. DOI 10.1016/0021-8693(81)90218-0 | MR 0617092

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