Hostname: page-component-848d4c4894-nmvwc Total loading time: 0 Render date: 2024-06-23T04:21:54.320Z Has data issue: false hasContentIssue false
  • English
  • Français

The Brauer characters of the sporadic simple Harada–Norton group and its automorphism group in characteristics 2 and 3

Part of: Representation theory of groups

Published online by Cambridge University Press:  01 August 2012

Gerhard Hiss ,
Jürgen Müller ,
Felix Noeske  and
Jon Thackray
Gerhard Hiss
Affiliation:
Lehrstuhl D für Mathematik, RWTH Aachen University, 52056 Aachen, Germany (email: Gerhard.Hiss@math.rwth-aachen.de)
Jürgen Müller
Affiliation:
Lehrstuhl D für Mathematik, RWTH Aachen University, 52056 Aachen, Germany (email: Juergen.Mueller@math.rwth-aachen.de)
Felix Noeske
Affiliation:
Lehrstuhl D für Mathematik, RWTH Aachen University, 52056 Aachen, Germany (email: Felix.Noeske@math.rwth-aachen.de)
Jon Thackray
Affiliation:
183 Huntington Road, Cambridge, CB3 0DL, United Kingdom (email: jgt@pobox.com)

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 determine the 2-modular and 3-modular character tables of the sporadic simple Harada–Norton group and its automorphism group.

MSC classification

Secondary: 20C20: Modular representations and characters 20C34: Representations of sporadic groups 20C40: Computational methods
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 15 , May 2012 , pp. 257 - 280
Copyright
Copyright © London Mathematical Society 2012

References

[1]Breuer, T., ‘CTblLib–a GAP package, version 1.1.3’, 2004, http://www.gap-system.org/Packages/ctbllib.html,.Google Scholar
[2]Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A. and Wilson, R. A., Atlas of finite groups: Maximal subgroups and ordinary characters for simple groups, with computational assistance from J. G. Thackray (Oxford University Press, Eynsham, 1985).Google Scholar
[3]Erdmann, K., ‘Algebras and semidihedral defect groups. II’, Proc. Lond. Math. Soc. (3) 60 (1990) no. 1, 123–165.CrossRefGoogle Scholar
[4] The GAP group, ‘GAP—groups, algorithms, and programming, version 4.4.12’, 2008, http://www.gap-system.org.Google Scholar
[5]Henke, A., Hiss, G. and Müller, J., ‘The 7-modular decomposition matrices of the sporadic O’Nan group’, J. Lond. Math. Soc. (2) 60 (1999) no. 1, 58–70.CrossRefGoogle Scholar
[6]Hiss, G., Jansen, C., Lux, K. and Parker, R. A., ‘Computational modular character theory’, http://www.math.rwth-aachen.de/MOC/CoMoChaT.Google Scholar
[7]Hiss, G. and Lux, K., Brauer trees of sporadic groups (Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1989).Google Scholar
[8]Jansen, C., Lux, K., Parker, R. and Wilson, R., ‘An atlas of Brauer characters’, London Mathematical Society Monographs, New Series 11 (The Clarendon Press, Oxford University Press, New York, 1995) Appendix 2 by T. Breuer and S. Norton, Oxford Science Publications.Google Scholar
[9]Koshitani, S. and Müller, J., ‘Broué’s abelian defect group conjecture holds for the Harada-Norton sporadic simple group HN’, J. Algebra 324 (2010) no. 3, 394–429.CrossRefGoogle Scholar
[10]Landrock, P., ‘The non-principal 2-blocks of sporadic simple groups’, Comm. Algebra 6 (1978) no. 18, 1865–1891.CrossRefGoogle Scholar
[11]Landrock, P., Finite group algebras and their modules, London Mathematical Society Lecture Note Series, vol. 84 (Cambridge University Press, Cambridge, 1983).CrossRefGoogle Scholar
[12]Lux, K., Müller, J. and Ringe, M., ‘Peakword condensation and submodule lattices: an application of the MEAT-AXE’, J. Symbolic Comput. 17 (1994) no. 6, 529–544.CrossRefGoogle Scholar
[13]Lux, K., Neunhöffer, M. and Noeske, F., ‘Condensation of homomorphism spaces’, LMS J. Comput. Math. 15 (2012) 140–157.CrossRefGoogle Scholar
[14]Lux, K., Noeske, F. and Ryba, Alexander J. E., ‘The 5-modular characters of the sporadic simple Harada-Norton group HN and its automorphism group HN.2’, J. Algebra 319 (2008) no. 1, 320–335.CrossRefGoogle Scholar
[15]Lux, K. and Pahlings, H., Representations of groups: A computational approach, Cambridge Studies in Advanced Mathematics 124 (Cambridge University Press, Cambridge, 2010).CrossRefGoogle Scholar
[16]Lux, K. and Wiegelmann, M., ‘Condensing tensor product modules’, The atlas of finite groups: ten years on (Birmingham, 1995), London Math. Soc. Lecture Note Ser. 249 (Cambridge University Press, Cambridge, 1998) 174–190.CrossRefGoogle Scholar
[17]Lux, K. and Wiegelmann, M., ‘Determination of socle series using the condensation method. Computational algebra and number theory: Proceedings of the Second Magma Conference (Milwaukee, WI, 1996)’, J. Symbolic Comput. 31 (2001) no. 1–2, 163–178.CrossRefGoogle Scholar
[18]Müller, J., On endomorphism rings and character tables, Habilitationsschrift, RWTH Aachen, 2003.Google Scholar
[19]Müller, J., Neunhöffer, M. and Noeske, F., ‘orb—a GAP package, Version 3.7’, 2011, http://www.gap-system.org/Packages/orb.html.Google Scholar
[20]Noeske, F., ‘Tackling the generation problem in condensation’, J. Algebra 309 (2007) no. 2, 711–722.CrossRefGoogle Scholar
[21]Noeske, F., ‘Matching simple modules of condensed algebras’, LMS J. Comput. Math. 11 (2008) 213–222.CrossRefGoogle Scholar
[22]Noeske, F., ‘Matching simple modules of condensation algebras’, LMS J. Comput. Math., to appear.Google Scholar
[23]Norton, S. P. and Wilson, R. A., ‘Maximal subgroups of the Harada–Norton group’, J. Algebra 103 (1986) no. 1, 362–376.CrossRefGoogle Scholar
[24]Olsson, J. B., ‘On 2-blocks with quaternion and quasidihedral defect groups’, J. Algebra 36 (1975) no. 2, 212–241.CrossRefGoogle Scholar
[25]Parker, R. A., ‘The computer calculation of modular characters (the meat-axe)’, Computational group theory (Durham, 1982) (Academic Press, London, 1984) 267–274.Google Scholar
[26]Ringe, M., ‘C-MeatAxe, version 2.4’, 2009, http://www.math.rwth-aachen.de/homes/MTX/.Google Scholar
[27]Ryba, A. J. E., ‘Computer condensation of modular representations. Computational group theory, Part 1’, J. Symbolic Comput. 9 (1990) no. 5–6, 591–600.CrossRefGoogle Scholar
[28]Thackray, J. G., ‘Modular representations of some finite groups’, PhD Thesis, University of Cambridge, 1981.Google Scholar
[29]Wilson, R., Walsh, P., Tripp, J., Suleiman, I., Parker, R., Norton, S., Nickerson, S., Linton, S., Bray, J. and Abbott, R., ‘ATLAS of finite group representations’, 2006, http://brauer.maths.qmul.ac.uk/Atlas/v3.Google Scholar
[30]Wilson, R. A., Parker, R. A., Nickerson, S., Bray, J. and Breuer, T., ‘AtlasRep—a GAP interface to the ATLAS of finite group representations, Version 1.4.0’, 2008, http://www.gap-system.org/Packages/atlasrep.html.Google Scholar
[31]Wilson, R. A., Thackray, J. G., Parker, R. A., Noeske, F., Müller, J., Lux, K., Lübeck, F., Jansen, C., Hiss, G. and Breuer, T., ‘The modular atlas project’, http://www.math.rwth-aachen.de/∼MOC.Google Scholar
[32]Wilson, R. A., ‘Standard generators for sporadic simple groups’, J. Algebra 184 (1996) no. 2, 505–515.CrossRefGoogle Scholar