A random base change algorithm for permutation groups
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Local expansion of vertex-transitive graphs and random generation in finite groups
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Nearly linear time algorithms for permutation groups with a small base
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
New methods for using Cayley graphs in interconnection networks
Discrete Applied Mathematics - Special double volume: interconnection networks
Constructing permutation representations for large matrix groups
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
A random base change algorithm for permutation groups
Journal of Symbolic Computation
Fast Monte Carlo algorithms for permutation groups
Selected papers of the 23rd annual ACM symposium on Theory of computing
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Fast Management of Permutation Groups I
SIAM Journal on Computing
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Constructing permutation representations for matrix groups
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
A new existence proof for Ly, the sporadic simple group of R. Lyons
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the second Magma conference
Database Management Systems
Scalable parallel coset enumeration: bulk definition and the memory wall
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
The product replacement algorithm is polynomial
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Computation with permutation groups
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
A disk-based parallel implementation for direct condensation of large permutation modules
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
A comparative analysis of parallel disk-based Methods for enumerating implicit graphs
Proceedings of the 2007 international workshop on Parallel symbolic computation
Fast multiplication of large permutations for disk, flash memory and RAM
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
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Group membership is a fundamental algorithm, upon which most other algorithms of computational group theory depend. Until now, group membership for permutation groups has been limited to ten million points or less. We extend the applicability of group membership algorithms to permutation groups acting on more than 100,000,000 points. As an example, we experimentally construct a group membership data structure for Thompson's group, acting on 143,127,000 points, in 36 minutes. More significantly, we require approximately 10 GB of RAM for the computation --- even though a single permutation of Thompson's group already requires half a gigabyte of storage.In addition, we propose a disk-based group membership algorithm with the promise of extending group membership to well over one billion (1,000,000,000) points. Such a disk-based algorithm has formerly been impossible, due in part to the lack of a practical disk-based algorithm for multiplying and taking inverses of such large permutations. Random access to disk is prohibitively expensive. We demonstrate the first practical disk-based implementation of the basic permutation operations. We also propose a disk-based architecture for group membership data structures.