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Normalizers of 2-subgroups in black-box groups

  • Peter Rowley (a1) and Paul Taylor (a2)
Abstract

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.

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References
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[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, 383401.
[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, 229240.
[3] Bates, C. J. and Rowley, P. J., ‘Normalizers of p-subgroups in finite groups’, Arch. Math. 92 (2009) 713.
[4] Bray, J. N., ‘An improved method for generating the centralizer of an involution’, Arch. Math. 74 (2000) 241245.
[5] Cannon, J. J. and Playoust, C., ‘An introduction to algebraic programming with Magma’, Draft (1997).
[6] Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A. and Wilson, R. A., Atlas of finite groups (Clarendon, Oxford, 1985).
[7] The GAP Group, ‘GAP—groups, algorithms, and programming, version 4.3’, 2002,http://www.gap-system.org.
[8] Gorenstein, D., Finite groups (Harper and Row, New York, 1968).
[9] Kantor, W. M. and Seress, A., ‘Black box classical groups’, Mem. Amer. Math. Soc. 149 (2001) no. 708,.
[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/.
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LMS Journal of Computation and Mathematics
  • ISSN: -
  • EISSN: 1461-1570
  • URL: /core/journals/lms-journal-of-computation-and-mathematics
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Supplementary materials

Rowley Supplementary Material
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