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On the ranks of Fischer group $Fi_{24}^{\,\prime}$ and the Baby Monster group $\mathbb{B}$ | ||
| International Journal of Group Theory | ||
| مقاله 2، دوره 8، شماره 1، خرداد 2019، صفحه 11-22 اصل مقاله (216.23 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2018.109973.1471 | ||
| نویسندگان | ||
| Mohammed Ali Faya Ibrahim1؛ Faryad Ali* 2؛ Mohammed A. Al-Kadhi2؛ Abdullah Mohammed Aljouiee3 | ||
| 1Najran University | ||
| 2Al Imam Mohammad Ibn Saud Islamic University | ||
| 3Al Imam Mohammed Ibn Saud Islamic University | ||
| چکیده | ||
| If $G$ is a finite group and $X$ a conjugacy class of elements of $G$, then we define $rank(G{:}X)$ to be the minimum number of elements of $X$ generating $G$. In the present article, we determine the ranks for the Fischer's simple group $Fi_{24}^{\prime}$ and the baby monster group $\mathbb{B}$. | ||
| کلیدواژهها | ||
| Fischer group $Fi_{24}^{؛ prime}$؛ rank؛ generating triple؛ Baby Monster group $mathbb{B}$ | ||
| مراجع | ||
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[1] F. Ali, On the ranks of F i 22 , Quaest. Math. , 37 (2014) 591{600. [2] F. Ali, On the ranks of O'N and Ly, Discrete Appl. Math. , 155 (2007) 394{399. [3] F. Ali and M. A. F. Ibrahim, On the ranks of the Conway groups C o 2 and C o 3 , J. Algebra Appl. , 4 (2005) 557{565. [4] F. Ali and M. A. F. Ibrahim, On the ranks of Conway group C o 1 , Proc. Japan Acad. Ser. A Math. Sci. , 81 (2005) 95{98. [5] F. Ali and M. A. F. Ibrahim, On the ranks of H S and M cL , Util. Math. , 70 (2006) 187{195. [6] F. Ali and M. A. F. Ibrahim, On the simple sp oradic group He generated by the (2 ; 3 ; t ) generators, Bul l. Malays. Math. Sci. Soc. (2) , 35 (2012) 745{753. [7] F. Ali and J. Mo ori, On the ranks of Janko groups J 1 , J2 , J 3 and J 4 , Quaestiones Mathematicae , 31 (2008) 37{44. [8] J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, An Atlas of Finite Groups , Oxford University Press, 1985. [9] 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. [10] L. Di Martino, M. A. Pellegrini and A. E. Zalesski, On generators and representations of the sp oradic simple groups, Comm. Algebra , 42 (2014) 880{908. [11] B. Fischer, Finite groups generated by 3-transp ositions. I, Invent. Math. , 13 (1971) 232{246. [12] B. Fischer, A note concerning f 3 ; 4 g -transposition groups , unpublished. [13] D. C. Hunt, The character table of the Baby Monster, unpublished. [14] S. Ganief, 2 -Generations of the sporadic simple groups , PhD Thesis, University of Natal 1997. [15] J. S. Leon and C. C. Sims, The existence and uniqueness of a simple group generated by f 3 ; 4 g -transp ositions, Bul l. Amer. Math. Soc. , 87 (1977) 1039{1040. [16] S. A. Linton and R. A. Wilson, The maximal subgroups of the Fischer groups F i 24 and F i ′ 24 , Proc. London Math. Soc. , 63 (1991) 113{164. [17] The GAP Group, GAP - Groups, Algorithms and Programming, Version 4.3 , Aachen, St Andrews, 2003, (http://www.gap-system.org) . [18] R. A. Wilson, Some subgroups of the Baby Monster, Invent. Math. , 89 (1987) 197{218. [19] R. A. Wilson, A new construction of the Baby Monster, and its applications, Bul l. London Math. Soc. , 25 (1993) 431{437. | ||
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