### ON THE CHARACTERIZABILITY OF SOME FAMILIES OF FINITE GROUP OF LIE TYPE BY ORDERS AND VANISHING ELEMENT ORDERS

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#### Abstract

where p ≥ 5, p ̸= 2m - 1, Ap(2), Cp(2), Dp(2), Dp+1(2) which for all of them p is an

odd prime and 2p - 1 is a Mersenne prime. Also, 2Dn(2) where 2n-1 + 1 is a Fermat

prime and n > 3, 2Dn(2) and Cn(2) where 2n + 1 is a Fermat prime. Then we give an

almost general result to recognize the non-solvability of finite group H by an anology

between orders and vanishing elemen orders of H and a finite simple group of Lie type.

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G. Y. Chen: A new characterization of G2(q), J. Southwest China Normal Univ., 21 (1996), 47-51.

G. Y. Chen: Characterization of Lie type group G2(q) by its order components, J. Southwest China Normal Univ., (Natural Science), 26 (5) (2001), 503-509.

G. Y. Chen: Characterization of 3D4(q), Southeast Asian Bulletin of Math.,25, (2001), 389-401.

G. Y. Chen and H. Shi: 2Dn(3) (9 ≤ n = 2m + 1 not a prime) can be characterized by its order components, J. Appl. Math. Comput., 19, (2005),355-362.

M. R. Darafsheh: Characterizability of group 2Dp(3) by its order components, where p ≥ 5 is a prime number not of the form 2m + 1, Acta Mathematica Sinica,English Series, 24 (7), (2008), 1117-1126.

M. R. Darafsheh: Characterization of groups Dp+1(2) and Dp+1(3) using order components, J. Korean Math. Soc., 47 (2), (2010), 311-329.

M. R. Darafsheh: On non-isomorphic groups with the same set of order components, J. Korean Math. Soc., 45 (1), (2008), 137-150.

M. R. Darafsheh and A. Mahmiani: A quantitative characterization of the linear group Lp+1(2) where p is a prime number, Kumamoto J. Math., 20,(2007), 33-50.

M. R. Darafsheh and A. Mahmiani: A characterization of the group 2Dn(2) where n = 2m + 1 ≥ 5, J. Appl. Math. Comput., 31, (2009), 447-457.

S. Dolfi, E. Pacifici, L. Sanus and P. Spiga: On the vanishing prime graph of finite groups, J. London Math. Soc., 82 (1) (2010), 167-183.

S. Dolfi, E.Pacifici, L. Sanus and P. Spiga: On the vanishing prime graph of solvable groups, J. Group Theory, 13 (2010), 189-206.

M. Foroudi Ghasemabadi, A. Iranmanesh and F. Mavadatpour: A new characterization of some finite simple groups, Siberian Math. J., 56, (2015), 78-82.

M. Foroudi Ghasemabadi, A. Iranmanesh and M. Ahanjideh: A new

characterization of some families of finite simple groups, Rend. Sem. Mat. Univ. Padova, European Mathematical Society, 137 (2017), 57-74.

N. Iiyori and H. Yamaki: Prime graph components of the simple groups of Lie type over the field of even characteristic, Proc. Japan Acad., 67, Ser. A, 1991.

A. Iranmanesh, S. H. Alavi and B. Khosravi: A characterization of PSL(3; q) where q is an odd prime power, J. Pure Appl. Algebra, 170, (2002), 243-254.

A. Iranmanesh, S. H. Alavi and B. Khosravi: A characterization of PSL(3; q) where q = 2n, Acta Math. App. Sinica (English Ser.), 18, (2002), 463-472.

A. Iranmanesh and B. Khosravi: A characterization of F4(q) where q is an odd prime power, Lecture Notes London Math. Soc., 304, (2003), 277-283.

A. Iranmanesh and B. Khosravi: A characterization of PSU(5; q), Int. Math.J., 3, (2003), 129-141.

A. Iranmanesh and B. Khosravi: A characterization of PSU(7; q), Int. J.Appl. Math., 15, (2004), 329-340.

A. Iranmanesh and B. Khosravi: A characterization of PSU(11; q), Canad.Math. Bull., 47, (2004), 530-539.

A. Iranmanesh and B. Khosravi: A characterization of F4(q) where q = 2n,(n > 1), Far East J. Math. Sci., (2000), 853-859.

A. Iranmanesh and B. Khosravi: A characterization of C2(q) where q > 5,Comment. Math. Univ. Carolin., 43, (2002), 9-21.

M. Khademi, M. R. Darafsheh: Characterization of the Group Dp(5) by order components, where p ≥ 5 is a prime number, Southeast Asian Bulletin of Mathematics, 37 (2013), 867-885.

M. Khatami and A. Babai: Recognition of some families of finite simple groups by order and set of orders of vanishing elements, Czechoslovak Math. J., 68,(2018), 121-130.

B. Khosravi, B. Khosravi and B. Khosravi: The number of isomorphism classes of finite groups with the set of order components of C4(q), Applicable Algebra in Engineering Comunication and Computing, 15, (2005), 349-359.

A. Khosravi and B. Khosravi: A new characterization of PSL(p; q), Comm.Algebra, 32 (6), (2004), 2325-2339.

A. Khosravi and B. Khosravi: A characterization of 2Dn(q), where n = 2m, Int. J. Math. Game Theory Algebra, 13, (2003), 253-266.

A. Khosravi and B. Khosravi: r-Recognizability of Bn(q) and Cn(q) where n = 2m, J. Pure App. Algebra, (2005), 149-165.

A. Khosravi and B. Khosravi: A characterizability of PSU(p + 1; q) by its order components, Rock Mountain J. Math., 36 (5), (2006), 1555-1575.

B. Khosravi, B. Khosravi and B. Khosravi: A new characterization of PSU(p; q), Acta Math. Hungar., 107 (3), (2005), 235-252.

B. Khosravi: A characterization of 2D4(q), Pure Math. Appl., 12, (2001),415-424.

B. Khosravi and B. Khosravi: A characterization of 2E6(q), Kumamoto J.Math., 16, (2003), 1-11.

B. Khosravi and B. Khosravi: A characterization of E6(q), Algebras Groups Geom., 19, (2002), 225-243.

B. Khosravi and B. Khosravi: Characterizability of PSL(p + 1; q) by its order components, Houston Journal of Mathematics, 32 (3), (2006), 683-700.

B. Khosravi and A. Iranmanesh: A characterization of 2Dp(3), where p = 2n + 1(n ≥ 2), Hadronic J. Suppl., 18 (4), (2003), 465-477.

M. Silvia Lucido and Ali Reza Moghaddamfar: Groups with complete prime graph connected components, J. Group Theory , (2004), 373-384.

A. V. Vasiliev and E. P. Vdovin: An adjacency criterion for the prime graph of a finite simple group, Algebra and Logic, 44 (6), (2005).

J. Zhang, Z. Li and C. Shao: Finite groups whose irreducible characters vanish only on elements of prime power order, International Electronic J. Algebra, 9 (2011), 114-123.

L. Zhang and W. Shi: New characterization of S4(q) by its noncommuting graph, Siberian Mathematical Journal, 50 (3), (2009), 533-540.

DOI: https://doi.org/10.22190/FUMI1903573P

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