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On a maximal subgroup of the Symplectic group $Sp(4,4)$ | ||
| AUT Journal of Mathematics and Computing | ||
| مقاله 2، دوره 4، شماره 1، 2023، صفحه 17-25 اصل مقاله (442.95 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2022.21693.1099 | ||
| نویسنده | ||
| Ayoub Basheer Mohammed Basheer* | ||
| School of Mathematical and Computer Sciences, University of Limpopo (Turfloop), P Bag X1106, Sovenga 0727, South Africa | ||
| چکیده | ||
| This paper is dealing with a split extension group of the form $2^{6}{:}(3 \times A_{5}),$ which is the largest maximal subgroup of the Symplectic group $Sp(4,4).$ We refer to this extension by $\overline{G}.$ We firstly determine the conjugacy classes of $\overline{G}$ using the coset analysis technique. The structures of inertia factor groups were determined. We then compute the Fischer matrices of $\overline{G}$ and apply the Clifford-Fischer theory to calculate the ordinary character table of this group. The Fischer matrices of $\overline{G}$ are all integer valued, with sizes ranging from 1 to 4. The full character table of $\overline{G}$ is $26 \times 26$ complex valued matrix and is given at the end of this paper. | ||
| کلیدواژه‌ها | ||
| Group extensions؛ Symplectic group؛ Inertia groups؛ Fischer matrices؛ Character table | ||
| مراجع | ||
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[4] A. B. M. Basheer, F. Ali, and M. L. Alotaibi, On a maximal subgroup of the Conway simple group Co3, Ital. J. Pure Appl. Math., (2020), pp. 357–372.
[5] A. B. M. Basheer and J. Moori, Fischer matrices of Dempwolff group 2 5.GL(5, 2), Int. J. Group Theory, 1 (2012), pp. 43–63.
[6] A. B. M. Basheer and J. Moori, On the non-split extension group 2 6·Sp(6, 2), Bull. Iranian Math. Soc., 39 (2013), pp. 1189–1212.
[7] A. B. M. Basheer and J. Moori, On a maximal subgroup of the Thompson simple group, Math. Commun., 20 (2015), pp. 201–218.
[8] A. B. M. Basheer and J. Moori, On the non-split extension 2 2n·Sp(2n, 2), Bull. Iranian Math. Soc., 41 (2015), pp. 499–518.
[9] A. B. M. Basheer and J. Moori, A survey on Clifford-Fischer theory, in Groups St Andrews 2013, vol. 422 of London Math. Soc. Lecture Note Ser., Cambridge Univ. Press, Cambridge, 2015, pp. 160–172.
[10] A. B. M. Basheer and T. T. Seretlo, On a group of the form 3 7 : Sp(6, 2), Int. J. Group Theory, 5 (2016), pp. 41–59.
[11] A. B. M. Basheer and J. Moori, Clifford-Fischer theory applied to a group of the form 2 1+6 − : ((31+2 : 8) : 2), Bull. Iranian Math. Soc., 43 (2017), pp. 41–52.
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[14] A. B. M. Basheer and J. Moori, On a maximal subgroup of the affine general linear group of GL(6, 2), Adv. Group Theory Appl., 11 (2021), pp. 1–30.
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