Nearly linear time algorithms for permutation groups with a small base
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
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
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Computation with permutation groups
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
Fast recognition of the nilpotency of permutation groups
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
A nearly linear algorithm for Sylow subgroups in small-base groups
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Constructing transitive permutation groups
Journal of Symbolic Computation
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The purpose of this note is to describe a new algorithm for finding blocks of imprimitivity for a permutation group G, operating on a domain &OHgr;.It runs in O(n log3|G| + ns log|G|) time, where n is the size of &OHgr; and s is the number of generators for G. In many situations it is therefore faster than Atkinson's method, which runs in O(n2s) time.A base of G is a subset B ⊆ &OHgr; such that only the identity of G fixes B pointwise. We call a family of groups small-base groups if they admit bases of size O(logc n) for some fixed constant c.If G belongs to a family of small-base groups, our algorithm runs in nearly linear time, namely in O(ns logc′ n). Beals recently gave an algorithm with the same worst case estimate. Our algorithm is simpler to implement and we expect faster practical performance.