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Abstract
Abstract.
Suppose that G be a finite group, and let N (G)
be the set of conjugacy class sizes of G. By Thompson’s conjecture, if H is a finite non abelian simple group, G is a finite group with a trivial center, and N (G) = N (H), then H and G are isomorphic. Chen et al. contributed interestingly to Thompsons conjecture under a weak condition. In this article, we investigate validity of Thompsons conjecture under a weak condition for the projective special unitary groups. This work implies that Thompsons conjecture holds for the PSU (3, q), where q is prime power.
References:-
References
N. Ahanjideh, Thompson’s conjecture for some finite simple groups, J. Algebra 344 (2011), 205-228.
A. K. Asboei, R. Mohammadyari, M. Rahimi New characterization of some linear group, Int. J. Industrial Mathematics, 8 (2), (2016), 165-170.
A. K. Asboei, R. Mohammadyari, Recognition alternating groups by their order and one conjugacy class length, J. Algebra. Appl, 15 (2), (2016), 1650021.
A. K. Asboei, R. Mohammadyari, Characterization of the alternating groups by their order and one conjugacy class length, Czechoslovak Math. J, 66 (141), (2016), 63-70.
A. K. Asboei, R. Mohammadyari, M. R. Darafsheh, The influence of order and conjugacy class length on the structure of finite groups, Hokkaido Math. J, 47 , (2018), 25-32.
G. Y. Chen, On Thompson’s conjecture, J. Algebra, 185(1) (1996), 184-193.
G. Y. Chen, On Frobenius and 2-Frobenius group, J. Southwest China Normal Univ, 20(5) (1995), 485-487.
G. Y. Chen, Futher refelections on Thompson’s conjecture, J. Algebra, 218(1) (1999), 276-285.
G. Y. Chen, A new characterization of sporadic simple groups, Algebra Colloq 3(1) (1996), 49-58.
Y. Chen, G. Y. Chen, Recognizing PSL(2, p) by its order and one special conjugacy class size, J. Inequal. Apple, (2012), 310.
Y. H. Chen, G. Y. Chen, Reconization of Alt10 and PSL(4, 4) by two special conjugacy class size, , Ital. J. Pure Appl. Math,29, (2012), 378-395.
J. H. Conway, R. T. Curtis, S.P. Norton, R.A. Parker and R.A. Wilson, Atlas of finite groups, Clarendon Press, New York, 1985.
M. Foroudi ghasemabadi, N. Ahanjideh, Characterization of the simple groups Dn(3) by prime graph and spectrum, Iran. J. Math. Sci. Inform, 7(1) (2012), 91- 106.
A. Iranmanesh, B. Khosravi, and S. H. Alavi, A characterization of PSU (3, q) for q > 5, Southeast Asian Bulletin of Mathematics, 26 (2002), 33-44.
N. Iiyory, H. Yamaki, Prime graph components of the simple groups of Lie type over the field of even characteristic, Acta Mathematica Sinica, English Series, 18(3)(2002), 463-472.
E. I. Khukhro, V. D. Mazarove, Unsolved Problems in Group Theory, The Kourovka Notebook, 17th edition, Sobolev Institute of Mathematics, Novosibrisk, (2010).
A. S. Kondratev and V. D. Mazarove, Recognition of Alternating groups of prime degree from their element orders, Sib. Math. J, 41 (2) (2000), 294-302.
J. B. Li, Finite groups with special conjugacy class sizes of generalized permutable subgroups, (2012), (Chongqing: Southwest University).
J. S. Williams, Prime graph components of finite groups, J. Algebra, 69 (2) (1981), 487-513.