Abstract
We prove that the projective special linear group \(L_2(q)\) is uniquely determined by its group order and its largest irreducible character degree when \(q\) is a prime or when \(q=2^a\) for an integer \(a\ge 2\) such that \(2^a-1\) or \(2^a+1\) is a prime.
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References
Bessenrodt, C.: On a Conjecture of Huppert for alternating groups. Arch. Math. 79, 401–403 (2002)
Brauer, R., Reynolds, W.F.: On a problem of E. Artin. Ann. Math. 68, 713–720 (1958)
Conway, J.H., Curtis, R.T., Norton, S.P., Parker, R.A., Wilson, R.A.: Atlas of Finite Groups. Oxford University Press, London (1985)
Hall, M.: The Theory of Groups. Macmillan, New York (1959)
Huppert, B.: Endliche Gruppen I, vol. 134 of Grund. Math. Wiss. Springer Verlag, Berlin Heidelberg (1967)
Isaacs, I.M.: Character Theory of Finite Groups. Academic Press, New York (1976)
Khosravi, B., Khosravi, B., Khosravi, B.: Recognition of PSL\((2, p)\) by order and some information on its character degrees where \(p\) is a prime. Monatsh Math. (2013). doi:10.1007/s00605-013-0582-2
Xu, H.J., Chen, G.Y., Yan, Y.X.: A new characterization of simple \({K}_3\)-groups by their orders and large degrees of their irreducible characters. Comm. Alg. (to appear)
Xu, H.J., Yan, Y.X., Chen, G.Y.: A new characterization of Mathieu-groups by the order and one irreducible character degree. J. Ineq. App. 209, 1–6 (2013)
Acknowledgments
The authors are grateful to Professor S. Dolfi for his valuable suggestions. The authors also thank the referee for his/her valuable suggestions who pointed out several linguistic inaccuracies. It should be said that we could not have polished the final version of this paper well without their outstanding efforts. This paper has been supported by the research Project NNSF of China (Grant Nos. 11101258, 11201401 and 11301218) and University of Jinan Research Funds for Doctors (XBS1335 and XBS1336)
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Communicated by J. S. Wilson.
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Jiang, Q., Shao, C. Recognition of \(L_2(q)\) by its group order and largest irreducible character degree. Monatsh Math 176, 413–422 (2015). https://doi.org/10.1007/s00605-014-0607-5
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DOI: https://doi.org/10.1007/s00605-014-0607-5