The Fischer-Clifford matrices of the inertia group 27:O- 6 (2) of a maximal subgroup 27:Sp6(2) in sp8(2)

Prins, Abraham; Fray, Richard

doi:10.22108/ijgt.2013.2049

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	The Fischer-Clifford matrices of the inertia group 2⁷:O^- ₆ (2) of a maximal subgroup 2⁷:Sp₆(2) in sp₈(2)
International Journal of Group Theory
مقاله 3، دوره 2، شماره 3، آذر 2013، صفحه 19-38 اصل مقاله (538.16 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2013.2049
نویسندگان
Abraham Prins^* ¹؛ Richard Fray²
¹Stellenbosch University
²University of the Western Cape
چکیده
The subgroups of symplectic groups which fix a non-zero vector of the underlying symplectic space are called affine subgroups., The split extension group $A(4)\cong 2^7{:}Sp_6(2)$ is the affine subgroup of the symplectic group $Sp_8(2)$ of index $255$‎. ‎In this paper‎, ‎we use the technique of the Fischer-Clifford matrices to construct the character table of the inertia group $2^7{:}O^{-}_{6}(2)$ of $A(4)$ of index $28$‎.
کلیدواژه‌ها
split extension؛ coset analysis؛ Fischer matrices

مراجع
Faryad Ali (2001) Fischer-Clifford Theory and Character Tables of Group Extensions PhD Thesis, University of Natal F. Ali and J. Moori (2004) Fischer-Clifford matrices and character table of the group $2^7:Sp_6(2)$ Int. J. Math. Game Theory and Algebra 14, 101-121 W. Bosma and J. J. Canon (1994) Handbook of Magma Functions Department of Mathematics, University of Sydney, November J. J. Cannon (1984) An introduction to the group theory language CAYLEY Computational Group Theory (M. Atkinson, eds), Academic Press, San Diego , 145-183 J. H. Conway, et al (1985) Atlas of Finite Groups Oxford University Press, Oxford B. Fischer (1991) Clifford-matrices Progr. Math., Michler G. O. and Ringel C.(eds), Birkhauser, Basel 95, 1-16 D. Gorenstein (1968) Finite Groups Harper and Row Publishers, New York I. M. Isaacs (1976) Character Theory of Finite Groups Academic Press, San Diego G. Karpilovsky (1992) Group Representations: Introduction to Group Representations and Characters Part B, North - Holland Mathematics Studies 175, Amsterdam 1 J. Moori (1981) On certain groups associated with the smallest Fischer group J. London Math. Soc. (2) 23, 61-67 J. Moori (1975) On the Groups $G^+$ and $\overline{G}$ of the forms $2^{10}:M_{22}$ and $2^{10}:\overline{M}_{22}$ PhD thesis, University of Birmingham J. Moori and Z. E. Mpono (2000) Fischer-Clifford matrices and the character table of a maximal subgroup of $\overline{F}_{22}$ Int. J. Math. Game Theory Algebra 10, 1-12 Z. Mpono (1998) Fischer-Clifford Theory and Character Tables of Group Extensions PhD Thesis, University of Natal A. L. Prins (2011) Fischer-Clifford Matrices and Character Tables of Inertia Groups of Maximal Subgroups of Finite Simple Groups of Extension Type PhD Thesis, University of the Western Cape M. Schonert, et al (1992) GAP - Groups, Algorithms and Programming Lehrstul D Fur Matematik, RWTH-Aachen N. S. Whitley (1994) Fischer Matrices and Character Tables of Group Extensions MSc Thesis, University of Natal K. Zimba (2005) Fischer-Clifford Matrices of the Generalized Symmetric Group and some Associated Groups PhD Thesis, University of KwaZulu Natal
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The Fischer-Clifford matrices of the inertia group 2⁷:O^- ₆ (2) of a maximal subgroup 2⁷:Sp₆(2) in sp₈(2)