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On a group of the form 37:Sp(6,2) | ||
| International Journal of Group Theory | ||
| مقاله 24، دوره 5، شماره 2، شهریور 2016، صفحه 41-59 اصل مقاله (282.29 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2016.8047 | ||
| نویسندگان | ||
| Ayoub Basheer* ؛ Jamshid Moori | ||
| North-West University (Mafikeng Campus) | ||
| چکیده | ||
| The purpose of this paper is the determination of the inertia factors, the computations of the Fischer matrices and the ordinary character table of the split extension $\overline{G}= 3^{7}{:}Sp(6,2)$ by means of Clifford-Fischer Theory. We firstly determine the conjugacy classes of $\overline{G}$ using the coset analysis method. The determination of the inertia factor groups of this extension involved looking at some maximal subgroups of the maximal subgroups of $Sp(6,2).$ The Fischer matrices of $\overline{G}$ are all listed in this paper and their sizes range between 2 and 10. The character table of $\overline{G},$ which is a $118\times 118\ \mathbb{C}$-valued matrix, is available in the PhD thesis of the first author, which could be accessed online. | ||
| کلیدواژهها | ||
| Group extensions؛ symplectic group؛ character table؛ inertia groups؛ Fischer matrices | ||
| مراجع | ||
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[1] A. B. M. Basheer, Clifford-Fischer Theory Applied to Certain Groups Associated with Symplectic, Unitary and Thompson Groups, Ph.D Thesis, University of KwaZulu-Natal, Pietermaitzburg, 2012. [2] A. B. M. Basheer and J. Mo ori, Fischer matrices of Dempwolff group $2^{5}{^{\cdot}}GL(5,2)$, Int. J. Group Theory, 1 no. 4 (2012) 43-63. [3] A. B. M. Basheer and J. Mo ori, On the non-split extension group $2^{6}{^{\cdot}}Sp(6,2)$, Bul l. Iranian Math. Soc., 39 (2013) 1189-1212. [4] A. B. M. Basheer and J. Moori, A survey on Clifford-Fischer Theory, London Mathematical Society Lecture Note Series, Groups St. Andrews 2013, Cambridge University Press, 422 (2015) 160-172. [5] J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, Atlas of Finite Groups, Clarendon Press, Oxford University Press, Eynsham, 1985. [6] A. H. Clifford, Representations induced in an invariant subgroup, Ann. of Math. (2), 38 (1937) 533-550. [7] B. Fischer, Clifford matrizen, manuscript, 1982. [8] B. Fischer, Unpublished manuscript, 1985. [9] B. Fischer, Clifford matrices, Representation theory of nite groups and nite-dimensional Lie algebras (eds G. O. Michler and C. M. Ringel; Birkhauser, Basel, (1991), 1-16. [10] The GAP Group, GAP-Groups, Algorithms, and Programming, Version 4.4.10; 2007. http://www.gap- system.org [11] Maxima, A Computer Algebra System, Version 5.18.1; 2009. http://maxima.sourceforge.net [12] J. Moori, On the Groups $G^{+}$ and $\overline{G}$ of the form $2^{10}{:}M_{22}$ and $2^{10}{:}\overline{M}_{22}$, PhD Thesis, University of Birmingham, 1975. [13] J. Mo ori, On certain groups asso ciated with the smallest Fischer group, J. London Math. Soc., 2 (1981) 61-67. [14] Z. E. Mp ono, Fischer Clifford Theory and Character Tables of Group Extensions , PhD Thesis, University of Natal, Pietermaritzburg, 1998. [15] U. Schiffer, Cliffordmatrizen, Diplomarb eit, Lehrstul D Fur Matematik, RWTH, Aachen, 1995. [16] R. A. Wilson et al., Atlas of nite group representations, http://brauer.maths.qmul.ac.uk/Atlas/v3/ . | ||
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