Abstract
In Project 6 we have encountered a way to construct groups via a permutation representation. In the early seventies this has been one of the main tools in constructing sporadic simple groups. However, the permutation representations of the large sporadic simple groups like the so-called Monster and Baby-Monster have too high degree to put them on a computer, see the Atlas [1]. For these groups one has to use different methods. Many of these large sporadic simple groups, including the Monster (see [4]), have been constructed as a matrix group. In this project we will show by means of a small example how one may proceed to construct a group as a matrix group.
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References
J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson (1985): ATLAS of Finite Groups, Clarendon Press, Oxford.
J.E. Humphreys (1990): Reflection Groups and Coxeter Groups, Cambridge Studies in Advanced Mathematics 29, Cambridge University Press.
W. Fulton and J. Harris (1991): Representation Theory: a First Course, Graduate Texts in Mathematics 129, Springer-Verlag, New York Berlin Heidelberg.
R.L. Griess: The Friendly Giant, Inventiones Math. 69, (1982), 1–102.
M. Schönert et al. (1994): GAP — Groups, Algorithms and Programming, version 3, release 4, Lehrstuhl D für Mathematik, RWTH Aachen.
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© 1999 Springer-Verlag Berlin Heidelberg
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Cohen, A.M., Cuypers, H., Riebeek, R. (1999). Explorations with the Icosahedral Group. In: Cohen, A.M., Cuypers, H., Sterk, H. (eds) Some Tapas of Computer Algebra. Algorithms and Computation in Mathematics, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03891-8_16
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DOI: https://doi.org/10.1007/978-3-662-03891-8_16
Publisher Name: Springer, Berlin, Heidelberg
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