Hostname: page-component-848d4c4894-nr4z6 Total loading time: 0 Render date: 2024-05-14T17:31:19.955Z Has data issue: false hasContentIssue false
  • English
  • Français

Normalizers of 2-subgroups in black-box groups

Part of: Representation theory of groups

Published online by Cambridge University Press:  01 August 2010

Peter Rowley  and
Paul Taylor
Peter Rowley
Affiliation:
School of Mathematics, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom (email: peter.j.rowley@manchester.ac.uk)
Paul Taylor
Affiliation:
School of Mathematics, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom (email: p.taylor@maths.manchester.ac.uk)

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.

In this paper we refine and extend the applicability of the algorithms in Bates and Rowley (Arch. Math. 92 (2009) 7–13) for computing part of the normalizer of a 2-subgroup in a black-box group.

Supplementary materials are available with this article.

MSC classification

Secondary: 20D06: Simple groups
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 13 , January 2010 , pp. 307 - 319
Copyright
Copyright © London Mathematical Society 2010

References

[1] Babai, L., Kantor, W. M., Pälfy, P. P. and Seress, A., ‘Black-box recognition of finite simple groups of Lie type by statistics of element orders’, J. Group Theory 5 (2002) no. 4, 383–401.CrossRefGoogle Scholar
[2] Babai, L. and Szemerdi, E., ‘On the complexity of matrix group problems I’, Proc. 25th IEEE Symp. Found. Comp. Sci.. Palm Beach, FL, 1984, 229–240.Google Scholar
[3] Bates, C. J. and Rowley, P. J., ‘Normalizers of p-subgroups in finite groups’, Arch. Math. 92 (2009) 7–13.Google Scholar
[4] Bray, J. N., ‘An improved method for generating the centralizer of an involution’, Arch. Math. 74 (2000) 241–245.CrossRefGoogle Scholar
[5] Cannon, J. J. and Playoust, C., ‘An introduction to algebraic programming with Magma’, Draft (1997).Google Scholar
[6] Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A. and Wilson, R. A., Atlas of finite groups (Clarendon, Oxford, 1985).Google Scholar
[7] The GAP Group, ‘GAP—groups, algorithms, and programming, version 4.3’, 2002,http://www.gap-system.org.Google Scholar
[8] Gorenstein, D., Finite groups (Harper and Row, New York, 1968).Google Scholar
[9] Kantor, W. M. and Seress, A., ‘Black box classical groups’, Mem. Amer. Math. Soc. 149 (2001) no. 708,.Google Scholar
[10] Wilson, R. A., Walsh, P. G., Tripp, J., Suleiman, I. A., Rogers, S., Parker, R. A., Norton, S. P., Linton, S. A. and Bray, J. N., ‘Atlas of finite group representations’,http://brauer.maths.qmul.ac.uk/Atlas/v3/.Google Scholar
Supplementary material: File

Rowley Supplementary Material

Supplementary material.zip

Download Rowley Supplementary Material(File)
File 31 MB