Hypergraph isomorphism and structural equivalence of Boolean functions
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Automorphism group computation and isomorphism testing in finite groups
Journal of Symbolic Computation
Polynomial-time normalizers for permutation groups with restricted composition factors
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
On the nlog n isomorphism technique (A Preliminary Report)
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Computation with permutation groups
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
Linear time algorithms for Abelian group isomorphism and related problems
Journal of Computer and System Sciences
Polynomial-time algorithms for permutation groups
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
Code equivalence and group isomorphism
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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We consider the problem of testing isomorphism of groups of order n given by Cayley tables. The trivial nlogn bound on the time complexity for the general case has not been improved upon over the past four decades. We demonstrate that the obstacle to efficient algorithms is the presence of abelian normal subgroups; we show this by giving a polynomial-time isomorphism test for groups without nontrivial abelian normal subgroups. This concludes a project started by the authors and J. A. Grochow (SODA 2011). Two key new ingredient are: (a) an algorithm to test permutational isomorphism of permutation groups in time, polynomial in the order and simply exponential in the degree; (b) the introduction of the "twisted code equivalence problem," a generalization of the classical code equivalence problem by admitting a group action on the alphabet. Both of these problems are of independent interest.