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projective general linear group; prime graph; recognition

References:

[1] Akhlaghi Z., Khosravi B., Khatami M.: **Characterization by prime graph of $ PGL(2,p^{k})$ where $p$ and $k>1$ are odd**. Internat. J. Algebra Comput. 20 (2010), no. 7, 847–873. DOI 10.1142/S021819671000587X | MR 2738548

[2] Aleeva M. R.: **On composition factors of finite groups having the same set of element orders as the group $U_3(q)$**. Sibirsk. Mat. Zh. 43 (2002), no. 2, 249–267 (Russian); translation in Siberian Math. J. 43 (2002), no. 2, 195–211. MR 1902821

[3] Aschbacher M., Seitz G. M.: **Involutions in Chevalley groups over fields of even order**. Nagoya Math. J. 63 (1976), 1–91. DOI 10.1017/S0027763000017438 | MR 0422401

[4] Buturlakin A. A.: **Spectra of finite linear and unitary groups**. Algebra Logika 47 (2008), no. 2, 157–173, 264 (Russian); translation in Algebra Logic 47 (2008), no. 2, 91–99. DOI 10.1007/s10469-008-9003-3 | MR 2438007

[5] Conway J. H., Curtis R. T., Norton S. P., Parker R. A., Wilson R. A.: **Atlas of Finite Groups**. Clarendon Press (Oxford), London, 1985. MR 0827219 | Zbl 0568.20001

[6] Darafsheh M. R., Farjami Y., Sadrudini A.: **A characterization property of the simple group $ PSL_4(5)$ by the set of its element orders**. Arch. Math. (Brno) 43 (2007), no. 1, 31–37. MR 2310122

[7] Higman G.: **Finite groups in which every element has prime power order**. J. Lond. Math. Soc. 32 (1957), 335–342. DOI 10.1112/jlms/s1-32.3.335 | MR 0089205

[8] Khatami M., Khosravi B., Akhlaghi Z.: **NCF-distinguishability by prime graph of $PGL(2, p)$, where $p$ is a prime**. Rocky Mountain J. Math. 41 (2011), no. 5, 1523–1545. DOI 10.1216/RMJ-2011-41-5-1523 | MR 2838076

[9] Kleidman P. B., Liebeck M. W.: **The Subgroup Structure of the Finite Classical Groups**. London Mathematical Society Lecture Note Series, 129, Cambridge University Press, Cambridge, 1990. MR 1057341

[10] Lucido M. S.: **Prime graph components of finite almost simple groups**. Rend. Sem. Mat. Univ. Padova 102 (1999), 1–22. MR 1739529

[11] Mahmoudifar A.: **On finite groups with the same prime graph as the projective general linear group $PGL(2, 81)$**. Transactions on Algebra and Its Applications 2 (2016), 43–49. MR 3746331

[12] Mahmoudifar A.: **On the unrecognizability by prime graph for the almost simple group $ PGL(2, 9)$**. Discuss. Math. Gen. Algebra Appl. 36 (2016), no. 2, 223–228. DOI 10.7151/dmgaa.1256 | MR 3594963

[13] Mahmoudifar A.: **Recognition by prime graph of the almost simple group $ PGL(2, 25)$**. J. Linear. Topol. Algebra 5 (2016), no. 1, 63–66. MR 3569945

[14] Mazurov V. D.: **Characterization of finite groups by sets of orders of their elements**. Algebra i Logika 36 (1997), no. 1, 37–53, 117 (Russian); translation in Algebra and Logic 36 (1997), no. 1, 23–32. MR 1454690

[15] Passman D. S.: **Permutation Groups**. W. A. Benjamin, New York, 1968. MR 0237627

[16] Perumal P.: **On the Theory of the Frobenius Groups**. Ph.D. Dissertation, University of Kwa-Zulu Natal, Pietermaritzburg, 2012.

[17] Praeger C. E., Shi W. J.: **A characterization of some alternating and symmetric groups**. Comm. Algebra 22 (1994), no. 5, 1507–1530. DOI 10.1080/00927879408824920 | MR 1264726

[18] Sajjadi M., Bibak M., Rezaeezadeh G. R.: **Characterization of some projective special linear groups in dimension four by their orders and degree patterns**. Bull. Iranian Math. Soc. 42 (2016), no. 1, 27–36. MR 3470934

[19] Shi W. J.: **On simple K$4$-groups**. Chinese Sci. Bull. 36 (1991), no. 7, 1281–1283 (Chinese). MR 1150578

[20] Simpson W. A., Frame J. S.: **The character tables for $ SL(3, q)$, $ SL(3, q^2)$, $ PSL(3, q)$, $ PSU(3, q^2)$**. Canadian. J. Math. 25 (1973), no. 3, 486–494. MR 0335618

[21] Srinivasan B.: **The characters of the finite symplectic group $ Sp(4,q)$**. Trans. Am. Math. Soc. 131 (1968), no. 2, 488–525. MR 0220845

[22] Vasil'ev A. V., Grechkoseeva M. A.: **On recognition by spectrum of finite simple linear groups over fields of characteristic $2$**. Sibirsk. Mat. Zh. 46 (2005), no. 4, 749–758 (Russian); translation in Siberian Math. J. 46 (2005), no. 4, 593–600. MR 2169394

[23] Williams J. S.: **Prime graph components of finite groups**. J. Algebra 69 (1981), no. 2, 487–513. DOI 10.1016/0021-8693(81)90218-0 | MR 0617092 | Zbl 0471.20013

[24] Yang N., Grechkoseeva M. A., Vasil'ev A. V.: **On the nilpotency of the solvable radical of a finite group isospectral to a simple group**. J. Group Theory 23 (2020), no. 3, 447–470. DOI 10.1515/jgth-2019-0109 | MR 4092939

[25] Zavarnitsine A. V.: **Finite simple groups with narrow prime spectrum**. Sib. Èlektron. Mat. Izv. 6 (2009), 1–12. MR 2586673 | Zbl 1289.20021

[26] Zavarnitsine A. V.: **Fixed points of large prime-order elements in the equicharacteristic action of linear and unitary groups**. Sib. Èlektron. Mat. Izv. 8 (2011), 333–340. MR 2876551

[27] Zavarnitsine A. V., Mazurov V. D.: **Element orders in coverings of symmetric and alternating groups**. Algebra Log. 38 (1999), no. 3, 296–315, 378 (Russian); translation in Algebra and Logic 38 (1999), no. 3, 159–170. MR 1766731

[28] HASH(0x126bfa8): **The GAP Group, GAP – Groups, Algorithms, and Programming, Version $4.11.1$**. 2021, https://www.gap-system.org