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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

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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

Information

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

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