Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-05T01:43:38.574Z Has data issue: false hasContentIssue false
  • English
  • Français

A Reduction Algorithm for Large-Base Primitive Permutation Groups

Published online by Cambridge University Press:  01 February 2010

Maska Law ,
Alice C. Niemeyer ,
Cheryl E. Praeger  and
Ákos Seress
Maska Law
Affiliation:
School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, Australia 6009, [email protected]
Alice C. Niemeyer
Affiliation:
School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, Australia 6009, [email protected]
Cheryl E. Praeger
Affiliation:
School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, Australia 6009, [email protected]
Ákos Seress
Affiliation:
Department of Mathematics, The Ohio State University, Columbus Ohio 43210, USA, [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.

The authors present a nearly linear-time Las Vegas algorithm that, given a large-base primitive permutation group, constructs its natural imprimitive representation. A large-base primitive permutation group is a subgroup of a wreath product of symmetric groups Sn and Sr in product action on r-tuples of k-element subsets of {1, …, n}, containing Anr. The algorithm is a randomised speed-up of a deterministic algorithm of Babai, Luks, and Seress.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 9 , 2006 , pp. 159 - 173
Copyright
Copyright © London Mathematical Society 2006

References

1. Babai, László, Cooperman, Gene, Finkelstein, Larry and Seress, Ákos, ‘Nearly linear time algorithms for permutation groups with a small base’. Proc. International Symposium on Symbolic and Algebraic Computation, ISSAC '91 (ed. Walt, S. M., ACM Press, New York, 1991) 200–209.Google Scholar
2. Babai, László, Luks, Eugene M. and Seress, Ákos, ‘Fast management of permutation groups’, Proc. 29th IEEE Symposium on Foundations of Computer Science, FOCS'88 (IEEE Computer Society Press, Los Alamitos. 1988) 272–282.Google Scholar
3. Babai, László, Luks, Eugene M. and Seress, Ákos, ‘Fast management of permutation groups I’, SIAM J. Computing 26 (1997) 1310–1342.CrossRefGoogle Scholar
4. Cooperman, Gene, Finkelstein, Larry and Sarawagi, Namita, ‘A random base change algorithm for permutation groups’, Proc. International Symposium on Symbolic and Algebraic Computation, ISSAC –90 (ed. Watanabe, S. and Nagata, M., ACM Press, New York. 1990) 161‘168.Google Scholar
5. Cameron, Peter J., ‘Finite permutation groups and finite simple groups’, Bull. London Math. Soc. 13 (1981) 1–22.CrossRefGoogle Scholar
6. Dixon, John D. and Mortimer, Brian, Permutation groups’, Graduate Texts in Math. 163 (Springer, New York, 1996).CrossRefGoogle Scholar
7. The GAP Group, ‘GAP-Groups, Algorithms, and Programming’. Version 4.4, 2005. http://www.gap-system.org.Google Scholar
8. Neunhöffer, Max and Seress, Ákos, ‘A data structure for a uniform approach to computations with finite groups’, Proc. International Symposium on Symbolic and Algebraic Computation, ISSAC '06 (ACM Press, New York. 2006). to appear.Google Scholar
9. Seress, Ákos, Permutation group algorithms, Cambridge Tracts in Mathematics 152 (Cambridge University Press, Cambridge, 2003).Google Scholar
10. Sims, Charles C., ‘Computation with permutation groups’, Proc. Second Symposium on Symbolic and Algebraic Manipulation, SYMSAC '71 (ed. Petrick, S. R., ACM Press, New York, 1971) 23–28.CrossRefGoogle Scholar