Characterization of some simple $K_4$-groups by some irreducible complex character degrees

Document Type: Research Paper

Authors

1 Shahrekord University

2 Shahrekord university

Abstract

In this paper‎, ‎we examine that some finite simple $K_4$-groups can be determined uniquely by their orders and one or two irreducible complex character degrees‎.

Keywords

Main Subjects


[1] J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, Atlas of nite groups, Clarendon, Oxford University Press, Eynsham, 1985.

[2] M. Herzog, On nite simple groups of order divisible by three primes only, J. Algebra, 10 (1968) 383-388.

[3] S. Heydari and N. Ahanjideh, A characterization of $PGL(2,p^n)$) by some irreducible complex character degrees, Publ. Inst. Math., 9 pages, In press.

[4] B. Hupp ert, Some simple groups which are determined by the set of their character degrees (I), I. Illinois J. Math., 44 (2000) 828-842.

[5] I. M. Isaacs, Character theory of nite groups, Corrected reprint of the 1976 original, [Academic Press, New York], AMS Chelsea Publishing, Providence, RI, 2006.

[6] Q. Jiang and C. Shao, Recognition of $L_2(q)$ by its group order and largest irreducible character degree, Monatsh. Math., 176 (2015) 413-422, DOI: 10.1007/s00605-014-0607-5.

[7] B. Khosravi, B. Khosravi and B. Khosravi, Recognition of $PSL(2,p)$ by order and some information on its character degrees where p is a prime, Monatsh. Math., 175 (2014) 277-282, DOI: 10.1007/s00605-013-0582-2 .

[8] A. S. Kondratev and I. V. Khramtsov, On nite tetraprimary groups, P. Steklov I. Math., 279 (2012) 43-61.

[9] M. A. Shahabi and H. Mohtadifar, The characters of the nite pro jective symplectic group $PSp(4‎, ‎q)$, Lond. Math. Soc. Lect. Note Ser., 305 (2001) 496-527.

[10] W. J. Shi, On simple $K_ 4$ -group, Chin. Sci. Bul l., 36 (1991) 1281-1283.

[11] H. Xu, G. Chen and Y. Yan, A new characterization of simple $K_3$-groups by their orders and large degrees of their irreducible characters, Comm. Algebra, 42 (2014) 5374{5380, DOI: 10.1080/00927872.2013.842242 .

[12] H. Xu, Y. Yan and G. Chen, A new characterization of Mathieu-groups by the order and one irreducible character degree, J. Inequal. Appl., (2013) pp. 6, DOI: 10.1186/1029-242X-2013-209 .