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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, maska@maths.uwa.edu.au
Alice C. Niemeyer
Affiliation:
School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, Australia 6009, alice@maths.uwa.edu.au
Cheryl E. Praeger
Affiliation:
School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, Australia 6009, praeger@maths.uwa.edu.au
Ákos Seress
Affiliation:
Department of Mathematics, The Ohio State University, Columbus Ohio 43210, USA, akos@math.ohio-state.edu

Abstract

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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

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