Graph isomorphism is in the low hierarchy
4th Annual Symposium on Theoretical Aspects of Computer Sciences on STACS 87
Arthur-Merlin games: a randomized proof system, and a hierarchy of complexity class
Journal of Computer and System Sciences - 17th Annual ACM Symposium in the Theory of Computing, May 6-8, 1985
Computing the structure of finite algebras
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Computing intersections and normalizersin soluble groups
Journal of Symbolic Computation
Finding Sylow normalizers in polynomial time
Journal of Algorithms
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Computing normalizers in permutation p-groups
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
Some algorithms for nilpotent permutation groups
Journal of Symbolic Computation
Polynomial-time computation in matrix groups
Polynomial-time computation in matrix groups
An improvement of GAP normalizer function for permutation groups
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
An improvement of a function computing normalizers for permutation groups
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
Polynomial-time isomorphism test for groups with no abelian normal subgroups
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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For an integer constant d 0, let Γd denote the class of finite groups all of whose nonabelian composition factors lie in Sd; in particular, Γd includes all solvable groups. Motivated by applications to graph-isomorphism testing, there has been extensive study of the complexity of computation for permutation groups in this class. In particular, set-stabilizers, group intersections, and centralizers have all been shown to be polynomial-time computable. The most notable gap in the theory has been the question of whether normalizers of subgroups can be found in polynomial time. We resolve this question in the affirmative. Among other new procedures, the algorithm requires instances of subspace-stabilizers for certain linear representations and therefore some polynomial-time computation in matrix groups.