In this paper, we give some presentations of some Mathieu groups by using some control subgroups and progenitors.
Keywords and phrases:Mathieu group, control subgroups, symmetric presentation.
Received February 13, 2011
References
[1]
J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups, Oxford, 1985.
[2]
A. M. Hammas, Symmetric presentations of some finite groups, Ph. D. Thesis, University of Birmingham, 1991.
[3]
R. T. Curtis, A. M. Hammas and J. N. Bray, A systematic approach to symmetric presentations. I, Involuntary generators, Math. Proc. Cambridge Philos. Soc. 119 (1996), 23-34.
[4]
M. Schnert et al., GAP, Groups, Algorithms and Programming, version 3 release 4 patchlevel 4, Lehrstuhl D für Mathematik, RWTH Aachen Alice Niemeyer, 1995.
[5]
Nesreen. A. Banaemah, Symmetric presentations of some finite groups, M. Sc., Taibah University, 2009.