A note on the affine subgroup of the symplectic group

Document Type : Research Paper


1 North-West University (Mafikeng) P Bag X2046, Mmabatho 2735, South Africa

2 University of KwaZulu-Natal Durban, South Africa


‎We examine the symplectic group $Sp_{2m}(q)$ and its corresponding affine subgroup‎. ‎We construct the affine subgroup and show that it is a split extension‎. ‎As an illustration of the above we study the affine subgroup $2^5{:}Sp_4(2)$ of the group $Sp_6(2)$‎.


Main Subjects

[1] F. Ali, Fischer-Clifford Theory for Split and Non-Split Group Extensions, Ph. D. thesis, University of Natal, Pieter-maritzburg, 2001.
[2] A. Basheer and J. Moori, On the non-split extension group 2Sp(6,2), Bull. Iranian Math. Soc., 39 (2013) 1189–1212.
[3] J. H. Conway, R.T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, Atlas of Finite Groups, Oxford University Press, Oxford, 1985.
[4] R. Gow, Some characters of affine subgroups of classical groups, J. London Math. Soc. (2), 2 (1976) 231–236.
[5] The GAP Group, GAP-Groups, Algorithms, and Programming, Version 4.4.
[6] J. Moori and T. Seretlo, On the Fischer-Clifford matrices of a maximal subgroup of the Lyons group Ly, Bul. of Iranian Math Soc., 39 (2013) 1037-1052.
[7] Z. E. Mpono, Fischer Clifford Theory and Character Tables of Group Extensions, Ph. D. thesis, University of Natal, Pietermaritzburg, 1998.
[8] B. G. Rodrigues, On the Theory and Examples of Group Extensions, Master’s thesis, University of Natal, Pieter-maritzburg, 1999.
[9] J. J. Rotman, An Introduction to the Theory of Groups, Fourth ed., Springer-Verlag, New York, Inc., 1995.
  • Receive Date: 02 April 2014
  • Revise Date: 10 November 2014
  • Accept Date: 12 November 2014
  • Published Online: 01 March 2016