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Mugala, Vasco, Chikopela, Dennis, Ng'ambi, Richard. (1403). On a group of the form $2^{11}:M_{24}$. نشریه مهندسی عمران امیرکبیر, 5(2), 167-193. doi: 10.22060/ajmc.2023.22289.1151
Vasco Mugala; Dennis Siwila Chikopela; Richard Ng'ambi. "On a group of the form $2^{11}:M_{24}$". نشریه مهندسی عمران امیرکبیر, 5, 2, 1403, 167-193. doi: 10.22060/ajmc.2023.22289.1151
Mugala, Vasco, Chikopela, Dennis, Ng'ambi, Richard. (1403). 'On a group of the form $2^{11}:M_{24}$', نشریه مهندسی عمران امیرکبیر, 5(2), pp. 167-193. doi: 10.22060/ajmc.2023.22289.1151
Mugala, Vasco, Chikopela, Dennis, Ng'ambi, Richard. On a group of the form $2^{11}:M_{24}$. نشریه مهندسی عمران امیرکبیر, 1403; 5(2): 167-193. doi: 10.22060/ajmc.2023.22289.1151

On a group of the form $2^{11}:M_{24}$

AUT Journal of Mathematics and Computing
مقاله 8، دوره 5، شماره 2، 2024، صفحه 167-193    اصل مقاله (527.41 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22060/ajmc.2023.22289.1151
نویسندگان
Vasco Mugala* ؛ Dennis Siwila Chikopela؛ Richard Ng'ambi
Mathematics Department, School of Mathematics and Natural Sciences, Copperbelt University, Zambia
چکیده
The Conway group $Co_{1}$ is one of the $26$ sporadic simple groups. It is the largest of the three Conway groups with order $4157776806543360000=2^{21}.3^9.5^4.7^2.11.13.23$ and has $22$ conjugacy classes of maximal subgroups. In this paper, we discuss a group of the form $\overline{G}=N\colon G$, where $N=2^{11}$ and $G=M_{24}$. This group $\overline{G}=N\colon G=2^{11}\colon M_{24}$ is a split extension of an elementary abelian group $N=2^{11}$ by a Mathieu group $G=M_{24}$. Using the computed Fischer matrices for each class representative $g$ of $G$ and ordinary character tables of the inertia factor groups of $G$, we obtain the full character table of $\overline{G}$. The complete fusion of $\overline{G}$ into its mother group $Co_1$ is also determined using the permutation character of $Co_1$.
کلیدواژه‌ها
Conway group؛ Conjugacy classes؛ Fischer matrices؛ Fusions؛ Permutation character
مراجع
  1. Ali, Fischer-Clifford matrices for split and non-split group extensions, PhD thesis, University of Natal, 2001.
  2. , The Fischer-Clifford matrices of a maximal subgroup of the sporadic simple group of Held, Algebra Colloq., 14 (2007), pp. 135–142.
  3. B. M. Basheer, Clifford-Fischer theory applied to certain groups associated with symplectic, unitary and Thompson groups, PhD thesis, University of Kwazulu-Natal, Pietermaritzburg.
  4. B. M. Basheer and J. Moori, Clifford-Fischer theory applied to a group of the form : 8) : 2), Bull. Iranian Math. Soc., 43 (2017), pp. 41–52.
  5. B. M. Basheer and T. T. Seretlo, On a group of the form 214 : Sp(6,2), Quaest. Math., 39 (2016), pp. 45–57.
  6. S. Chikopela, Clifford-Fischer matrices and character tables of certain group extensions associated with M22:2,M24 and HS:2, Master’s thesis, Mafikeng Campus of the North-West University, 2016.
  7. S. Chikopela and T. Seretlo, On a maximal subgroup 26:(3.S6) of M24, Math. Interdisc. Res., 7 (2022), pp. 197–216.
  8. Chileshe, Irreducible characters of sylow p-subgroups of GL(n,pk), Master’s thesis, North-West University, 2013.
  9. , Irreducible characters of Sylow p-subgroups associated with some classical linear groups, PhD thesis, North-West University, 2016.
  10. Chileshe, J. Moori, and T. T. Seretlo, On a maximal parabolic subgroup of (2), Bull. Iranian Math. Soc., 44 (2018), pp. 159–181.
  11. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson, ATLAS of finite groups, Oxford University Press, Eynsham, 1985. Maximal subgroups and ordinary characters for simple groups, With computational assistance from J. G. Thackray.
  12. GAP Group, GAP – Groups, Algorithms, and Programming, Version 4.10.2, 2019. [Online; accessed 11-Dec- 2023].
  13. Kapata, Clifford-Fischer theory applied to split and non-split extensions, Msc Thesis, University of Zambia, Lusaka, 2021.
  14. Moori, On The Groups G+ and G of the forms 210:M22 and 210: M¯22, PhD thesis, University of Birmingham, 1975.
  15. E. Mpono, Fischer-Clifford theory and character tables of group extensions, PhD thesis, University of Natal, 1998.
  16. Mugala, Clifford-Fischer theory applied to certain group extensions associated with Conway group Co1, symplectic groups SP6(2) and SP8(2), MSc Thesis, Copperbelt University, Kitwe, 2022.
  17. L. Prins, Fischer-Clifford theory applied to a non-split extension group 25·GL4(2), Palest. J. Math., 5 (2016), pp. 71–82.
  18. T. Seretlo, Fischer-Clifford matrices and character tables of certain groups associated with simple groups (2), PhD thesis, University of Kwazulu-Natal, 2012.
  19. Wilson, P. Walsh, J. Tripp, I. Suleiman, R. Parker, S. Norton, S. Nickerson, S. Linton, J. Bray, and R. Abbott, Atlas of finite group representation.
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