It is demonstrated that every finite group G with the same order and degree pattern as \( {O}_8^{-}(q) \)for certain q is necessarily isomorphic to the group \( {O}_8^{-}(q). \)
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B. Akbari and A. R. Moghaddamfar, “Recognizing by order and degree pattern of some projective special linear groups,” Int. J. Algebra Comput., 22, No. 6, 1–22 (2012).
A. A. Buturlakin, “Spectra of finite symplectic and orthogonal groups,” Siber. Adv. Math., 21, No. 3, 176–210 (2011).
Y. H. Chen, G. Y. Chen, and J. B. Li, “Recognizing simple K4-groups by few special conjugacy class sizes,” Bull. Malays. Math. Sci. Soc., 38, No. 1, 51–72 (2015).
M. R. Darafsheh, G. R. Rezaeezadeh, M. Bibak, and M. Sajjadi, “OD-characterization of almost simple groups related to 2E6(2),” Adv. Algebra, 6, 45–54 (2013).
M. R. Darafsheh, G. R. Rezaeezadeh, M. Sajjadi, and M. Bibak, “OD-characterization of almost simple groups related to U3(17),” Quasigroups Related Syst., 21, 49–58 (2013).
A. Daneshkhah and Y. Jalilian, “A characterization of some projective special linear groups,” Ital. J. Pure Appl. Math., 38, 32–44 (2017).
A. R. Moghaddamfar, A. R. Zokayi, and M. R. Darafsheh, “A characterization of finite simple groups by the degree of vertices of their prime graphs,” Algebra Colloq., 12, No. 3, 431–442 (2005).
G. R. Rezaeezadeh, M. Bibak, and M. Sajjad, “Characterization of projective special linear groups in dimension three by their orders and degree patterns,” Bull. Iran. Math. Soc., 41, No. 3, 551–580 (2015).
G. R. Rezaeezadeh, M. R. Darafsheh, M. Sajjadi, and M. Bibak, “OD-characterization of almost simple groups related to L3(25),” Bull. Iran. Math. Soc., 40, No. 3, 765–790 (2014).
G. R. Rezaeezadeh, M. R. Darafsheh, M. Bibak, and M. Sajjadi, “OD-characterization of almost simple groups related to D4(4),” Iran. J. Math. Sci. Inform., 10, No. 1, 23–43 (2015).
D. J. S. Robinson, A Course in the Theory of Groups, 2nd ed., Springer-Verlag, New York, etc. (2003).
M. Sajjadi, M. Bibak, and G. R. Rezaeezadeh, “Characterization of some projective special linear groups in dimension four by their orders and degree patterns,” Bull. Iran. Math. Soc., 42, No. 1, 27–36 (2016).
A. V. Vasil’ev, “On connection between the structure of a finite group and the properties of its prime graph,” Sib. Math. J., 46, No. 3, 396–404 (2005).
J. S. Williams, “Prime graph components of finite group,” J. Algebra, 69, 487–513 (1981).
Y. Yan, G. Chen, and L. Wang, “OD-characterization of the automorphism groups of \( {O}_{10}^{\pm }(2) \),” Ind. J. Pure Appl. Math., 43, No. 3, 183–195 (2012).
A. Zavarnitsine, “Finite simple groups with narrow prime spectrum,” Sib. Elektron. Mat. Izv., 6, 1–12 (2009).
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 6, pp. 743–751, June, 2022. Ukrainian DOI: https://doi.org/10.37863/umzh.v74i6.2357.
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Bibak, M., Rezaeezadeh, G.H. Characterization by Order and Degree Pattern of the Simple Groups \( {O}_8^{-}(q) \) for Certain q. Ukr Math J 74, 849–858 (2022). https://doi.org/10.1007/s11253-022-02112-3
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DOI: https://doi.org/10.1007/s11253-022-02112-3