Breaking the nlog n Barrier for Solvable-Group Isomorphism

@article{Rosenbaum2013BreakingTN,
  title={Breaking the nlog n Barrier for Solvable-Group Isomorphism},
  author={David J. Rosenbaum},
  journal={ArXiv},
  year={2013},
  volume={abs/1205.0642}
}
  • David J. Rosenbaum
  • Published 2013
  • Mathematics, Computer Science, Physics
  • ArXiv
  • We consider the group isomorphism problem: given two finite groups G and H specified by their multiplication tables, decide if G and H are isomorphic. The n^(log n) barrier for group isomorphism has withstood all attacks --- even for the special cases of p-groups and solvable groups --- ever since the n^(log n + O(1)) generator-enumeration algorithm. In this work, we present the first significant improvement over n^(log n) by showing that group isomorphism is n^((1 / 2) log_p n + O(1)) Turing… CONTINUE READING

    Citations

    Publications citing this paper.
    SHOWING 1-10 OF 13 CITATIONS

    Beating the generator-enumeration bound for p-group isomorphism

    VIEW 2 EXCERPTS
    CITES BACKGROUND

    Beating the Generator-Enumeration Bound for Solvable-Group Isomorphism

    VIEW 1 EXCERPT
    CITES METHODS

    On the Complexity of Group Isomorphism

    • Fabian Wagner
    • Computer Science, Mathematics
    • Electronic Colloquium on Computational Complexity
    • 2011

    Algorithms for Group Isomorphism via Group Extensions and Cohomology

    Group Isomorphism with Fixed Subnormal Chains

    VIEW 2 EXCERPTS
    CITES BACKGROUND

    Bidirectional Collision Detection and Faster Deterministic Isomorphism Testing

    VIEW 9 EXCERPTS
    CITES BACKGROUND & METHODS

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 55 REFERENCES

    Linear time algorithms for Abelian group isomorphism and related problems

    VIEW 1 EXCERPT

    On the Complexity of Group Isomorphism

    • Fabian Wagner
    • Computer Science, Mathematics
    • Electronic Colloquium on Computational Complexity
    • 2011
    VIEW 2 EXCERPTS

    Graph Isomorphism is not AC^0 reducible to Group Isomorphism

    VIEW 1 EXCERPT

    On the nlog n isomorphism technique (A Preliminary Report)

    VIEW 1 EXCERPT