A compact representation for permutation groups
Journal of Algorithms
A new base change algorithm for permutation groups
SIAM Journal on Computing
Fast group membership using a strong generating test for permutation groups
Proceedings of the third conference on Computers and mathematics
A strong generating test and short presentations for permutation groups
Journal of Symbolic Computation - Special issue on computational group theory: part 2
Computation with permutation groups
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
A random base change algorithm for permutation groups
ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Structure forest and composition factors for small base groups in nearly linear time
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
A fast cyclic base change for permutation groups
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
An elementary algorithm for computing the composition factors of a permutation group
ISSAC '93 Proceedings of the 1993 international symposium on Symbolic and algebraic computation
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The construction of point stabilizer subgroups is a problem which has been studied intensively. [1, 4, 5, 10, 11, 12, 14] This work describes a general reduction of certain group constructions to the point stabilizer problem. Examples are given for the centralizer, the normal closure, and a restricted group intersection problem. For the normal closure problem, this work provides an alternative to current algorithms, which are limited by the need for repeated closures under conjugation. For the centralizer and restricted group intersection problems, one can use an existing point stabilizer sequence along with a recent base change algorithm [2] to avoid generating a new point stabilizer sequence. This reduces the time complexity by at least an order of magnitude. Algorithms and theoretical time estimates for the special case of a small base are also summarized. An implementation is in progress.