Characterization by order and degree pattern of the simple groups $O^{-}_{8}(q)$ for certain $q$
Abstract
UDC 512.5
In this paper, 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 $O^{-}_{8}(q)$.
References
B. Akbari, A. R. Moghaddamfar, Recognizing by order and degree pattern of some projective special linear groups, Int. J. Algebra Comput., 22, № 6, 1 – 22 (2012), https://doi.org/10.1142/S0218196712500518 DOI: https://doi.org/10.1142/S0218196712500518
A. A. Buturlakin, Spectra of finite symplectic and orthogonal groups, Siberian Adv. Math., 21, № 3, 176 – 210 (2011), https://doi.org/10.3103/s1055134411030035 DOI: https://doi.org/10.3103/S1055134411030035
Y. H. Chen, G. Y. Chen, J. B. Li, Recognizing simple $K_4$ -groups by few special conjugacy class sizes, Bull. Malays. Math. Sci. Soc., 38, № 1, 51 – 72 (2015), https://doi.org/10.1007/s40840-014-0003-2 DOI: https://doi.org/10.1007/s40840-014-0003-2
M. R. Darafsheh, G. R. Rezaeezadeh, M. Bibak, M. Sajjadi, $OD$-characterization of almost simple groups related to $^2E_6(2)$, Adv. Algebra, 6, 45 – 54 (2013).
M. R. Darafsheh, G. R. Rezaeezadeh, M. Sajjadi, M. Bibak, $OD$-characterization of almost simple groups related to $U_3(17)$, Quasigroups and Related Systems, 21, 49 – 58 (2013).
A. Daneshkhah, Y. Jalilian, A characterization of some projective special linear groups, Ital. J. Pure and Appl. Math., 38, 32 – 44 (2017).
A. R. Moghaddamfar, A. R. Zokayi, M. R. Darafsheh, A characterization of finite simple groups by the degree of vertices of their prime graphs, Algebra Colloq., 12, № 3, 431 – 442 (2005), https://doi.org/10.1142/S1005386705000398 DOI: https://doi.org/10.1142/S1005386705000398
G. R. Rezaeezadeh, M. Bibak, M. Sajjad, Characterization of projective special linear groups in dimension three by their orders and degree patterns, Bull. Iranian Math. Soc., 41, № 3, 551 – 580 (2015).
G. R. Rezaeezadeh, M. R. Darafsheh, M. Sajjadi, M. Bibak, $OD$-characterization of almost simple groups related to $L_3(25)$, Bull. Iranian Math. Soc., 40, № 3, 765 – 790 (2014).
G. R. Rezaeezadeh, M. R. Darafsheh, M. Bibak, M. Sajjadi, $OD$-characterization of almost simple groups related to $D_4(4)$, Iran. J. Math. Sci. and Inform., 10, № 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, G. R. Rezaeezadeh, Characterization of some projective special linear groups in dimension four by their orders and degree patterns, Bull. Iranian Math. Soc., 42, № 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, № 3, 396 – 404 (2005). DOI: https://doi.org/10.1007/s11202-005-0042-x
J. S. Williams, Prime graph components of finite group, J. Algebra, 69, 487 – 513 (1981), https://doi.org/10.1016/0021-8693(81)90218-0 DOI: https://doi.org/10.1016/0021-8693(81)90218-0
Y. Yan, G. Chen, L. Wang, $OD$-characterization of the automorphism groups of $O^±_{10}(2)^1$, Indian J. Pure and Appl. Math., 43, № 3, 183 – 195 (2012), https://doi.org/10.1007/s13226-012-0011-6 DOI: https://doi.org/10.1007/s13226-012-0011-6
A. Zavarnitsine, Finite simple groups with narrow prime spectrum, Sib. Elektron. Mat. Izv., 6, 1 – 12 (2009).
Copyright (c) 2022 gholamreza rezaeezadeh
This work is licensed under a Creative Commons Attribution 4.0 International License.
