Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-23T15:36:09.487Z Has data issue: false hasContentIssue false
  • English
  • Français

The Character Table of a Maximal Subgroup of the Monster

Published online by Cambridge University Press:  01 February 2010

R. W. Barraclough  and
R. A. Wilson
R. W. Barraclough
Affiliation:
School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London El 4NS, United Kingdom, [email protected], http://www.maths.qmul.ac.uk/~rwb
R. A. Wilson
Affiliation:
School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London El 4NS, United Kingdom, [email protected]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We calculate the character table of the maximal subgroup of the Monster N(3B) isomorphic to a group of shape 3+1+12 · 2 · Suz: 2, and also of the group 31+12 : 6 · Suz · 2, which has the former as a quotient.The strategy is to induce characters from the inertia groups in 31+12 : 6 · Suz : 2 of characters of 31+12. We obtain the quotient map to N(3B) computationally, and our careful concrete approach allows us to produce class fusions between our tables and various tables in the GAP library.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 10 , 2007 , pp. 161 - 175
Copyright
Copyright © London Mathematical Society 2007

References

1.Barraclough, R. W. and Wilson, R. A., ‘Conjugacy class representatives for the Monster group’, LMS J. Comput. Math. 8 (2003) 203–216, http://www.lms.ac.uk/jcm/8/lms2005-007.Google Scholar
2.Bray, J. N. and Wilson, R. A., ‘Explicit construction of maximal subgroups of ihe Monster’, J. Algebm, to appear.Google Scholar
3.Breuer, ThomasManual for the GAP character table library, Version 1.1 (Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule. Aachen. Germany, 2004).Google Scholar
4.Conway, J. H., ‘A simple construction for the Fischer-Griess monster group’, Invent. Math. 79 (1983) 313–340.Google Scholar
5.Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A. and Wilson, R. A., with computational assistance from Thackray, J. G., An ATLAS of finite groups. Maximal subgroups and ordinary characters for simple groups (Oxford University Press, Eynsham. 1983).Google Scholar
6.The GAP Group, ‘GAP – groups, algorithms, and programming’. Version 4.3 (2002), http://www.gap-system.org.Google Scholar
7.Griess, R. L., ‘The friendly giant’, Invent. Math. 69 (1982) 1–102.CrossRefGoogle Scholar
8.Holmes, P. E. and Wilson, R. A.. ‘A new maximal subgroup of the Monster’, J. Algebra 231 (2002) 433–447.Google Scholar
9.Holmes, P. E. and Wilson, R. A.. ‘A computer construction of the monster using 2-local subgroups’, J. London Math. Soc. 67 (2003) 349–364.CrossRefGoogle Scholar
10.Holmes, P. E. and Wilson, R. A., ‘PSL2(59) is a subgroup of the Monster’, J. London Math. Soc. (2) 69 (2004) 141–132.CrossRefGoogle Scholar
11.Isaacs, I. M., Character theory of finite groups (Dover, 1994).Google Scholar
12.Jansen, C., Lux, K., Parker, R. A. and Wilson, R. A., An Atlas of Brauer characters, London Mathematical Society Monographs (N.S.) 11 (Oxford University Press. 1993).Google Scholar
13.Jansen, C.and Müller, J., ‘The 3-modular decomposition numbers of the sporadic simple Suzuki group’, Comm. Algebra 23 (1997) 2437–2438.CrossRefGoogle Scholar
14.Lehrstuhl D für Mathematik, RWTH Aachen. ‘The Meataxe–computing with modular representations’, 2004, http://www.math.rwth-aachen.de/homes/MTX/.Google Scholar
15.Linton, S. A., Parker, R. A., Walsh, P. and Wilson, R. A., ‘Computer construction of the monster’, J. Group Theory 1 (1998) 307–337.Google Scholar
16.Lübeck, F. et at.. ‘The modular atlas’. 2004. http://www.math.rwth-aachen.de/~MOC.Google Scholar
17.Lübeck, F., ‘Conway polynomials for finite fields’, 2004, http://www.math.rwth-aachen.de:8001/~Frank.Luebeck/data/ConwayPol.Google Scholar
18.Norton, S. P., ‘Counting nets in the Monster’, Combinatorics and geometry, Durham, 2001 (ed.Ivanov, A. A., Liebeck, M. W. and Saxl, J., World Science Publishing Company, 2003) 227–232.Google Scholar
19.Seress, A., Permutation group algorithms (Cambridge University Press, 2003).CrossRefGoogle Scholar
20.Stather, M.. ‘Computing in matrix groups’. Seminars at ‘Groups St Andrews 2003’ and Magma Workshop on Group Theory and Algebraic Geometry, Warwick, 2005; see http://www.Baths.warwick.ac.uk/~dih/magmaOS.html.Google Scholar
21.Suleiman, I. A. I., Walsh, P. G. and Wilson, R. A., ‘Conjugacy classes in sporadic simple groups’, Comm. Algebra 28 (2000) 3200–3222.CrossRefGoogle Scholar
22.Unger, W., ‘Computing the character table of a finite group’, J. Symbolic Compul. 41 (2006) 847–862.CrossRefGoogle Scholar
23.University of Sydney, ‘The Magma Handbook’, 2004, http://magma.maths.usyd.edu.au/magma/htmlhelp/MAGMA.htm.Google Scholar
24.Wilson, R. A., ‘Standard generators for sporadic simple groups’, J. Algebra 184 (1996) 005–313.CrossRefGoogle Scholar
Supplementary material: File

JCM 10 Barraclough and Wilson Appendix A readme

Barraclough and Wilson Appendix A readme.txt

Download JCM 10 Barraclough and Wilson Appendix A readme(File)
File 569 Bytes
Supplementary material: File

JCM 10 Barraclough and Wilson Appendix A

Barraclough and Wilson Appendix A

Download JCM 10 Barraclough and Wilson Appendix A(File)
File 147.9 KB