The conjugacy class ranks of $M_{24}$

Document Type: Research Paper

Author

University of South Africa

Abstract

$M_{24}$ is the largest Mathieu sporadic simple group of order $244 823 040 = 2^{10} {\cdot} 3^3 {\cdot} 5 {\cdot} 7 {\cdot} 11 {\cdot} 23$ and contains all the other Mathieu sporadic simple groups as subgroups. The object in this paper is to study the ranks of $M_{24}$ with respect to the conjugacy classes of all its nonidentity elements.

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References

[1] F. Ali, On the ranks of O'N and Ly, Discrete Appl. Math., 155 (2007) 394-399.

[2] F. Ali, On the ranks of Fi22 , Quaest. Math., 37 (2014) 591-600.

[3] F. Ali and J. Mo ori, On the ranks of the Janko groups J1, J2, J3 and J4 , Quaest. Math., 31 (2008) 37-44.

[4] J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, Atlas of Finite Groups, Oxford University Press, New York, 1985.

[5] M. D. E. Conder, R. A. Wilson and A. J. Woldar, The symmetric genus of sp oradic groups, Proc. Amer. Math. Soc., 116 (1992) 653-663.

[6] S. M. Ganief, 2-Generations of the Sporadic Simple Gropups, PhD Thesis, University of Natal, South Africa, 1997.

[7] S. Ganief and J. Moori, (2, 3, t)-generations for the Janko group J3, Comm. Algebra, 23 (1995) 4427-4437.

[8] The GAP Group, GAP-Groups, Algorithms, and Programming, Version 4.4.10; 2007. www.gap-system.org.

[9] www.math.rwth-aachen.de/homes/MOC/decomp osition/ .

[10] C. Jansen, K. Lux, R. Parker and R. Wilson, An Atlas of Brauer Characters, Oxford University Press Inc., New York, 1995.

[11] J. Mo ori, On the ranks of the Fischer group F22, Math. Japonica, 43 (1996) 365-367.

[12] J. Mo ori, On the ranks of Janko groups J1, J2, J3, article presented at the 41st annual congress of the South African Mathematical So ciety, Rand Afrikaans University, Johannesburg, 1998.

[13] Z. Mp ono, Triple generations and connected comp onents of Brauer graphs in M24 , Southeast Asian Bull. Math., 41 (2017) 65-89.

[14] A. J. Woldar, 3/2-generarion of the sp oradic simple groups, Comm. Algebra, 22 (1994) 675-685.