A random base change algorithm for permutation groups
ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
Nearly linear time algorithms for permutation groups with a small base
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
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
Selecting base points for the Schreier-Sims algorithm for matrix groups
Journal of Symbolic Computation
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Fast Management of Permutation Groups I
SIAM Journal on Computing
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
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
AAECC-8 Proceedings of the 8th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Computation with permutation groups
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
TOP-C: a task-oriented parallel C interface
HPDC '96 Proceedings of the 5th IEEE International Symposium on High Performance Distributed Computing
Memory-based and disk-based algorithms for very high degree permutation groups
ISSAC '03 Proceedings of the 2003 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
Harnessing parallel disks to solve Rubik's cube
Journal of 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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We outline a distributed, disk-based technique for computing over very large matrix groups. This technique is used to compute a permutation representation for the Baby Monster, a sporadic simple group that acts on 13,571,955,000 points. Its group order is approximately 4 × 1033. This is a landmark because it is 100 times larger than any previous construction of a permutation representation. By using the computed on-disk data structures, computation over the Baby Monster is now feasible using the distributed disks of a cluster. Our work allows researchers to use either a matrix, a permutation, or a word representation for computing over the Baby Monster where previously only a matrix representation was available. The methodology is demonstrated by using as a signature the image of a vector that is stabilized by the maximal subgroup. The technique extends to finite simple groups and to other groups, through other signatures.