Beating the generator-enumeration bound for p-group isomorphism

@article{Rosenbaum2015BeatingTG,
  title={Beating the generator-enumeration bound for p-group isomorphism},
  author={David J. Rosenbaum and F. Wagner},
  journal={Theor. Comput. Sci.},
  year={2015},
  volume={593},
  pages={16-25}
}
  • David J. Rosenbaum, F. Wagner
  • Published 2015
  • Computer Science, Mathematics
  • Theor. Comput. Sci.
  • We consider the group isomorphism problem: given two finite groups G and H specified by their multiplication tables, decide if G cong H. For several decades, the n^(log_p n + O(1)) generator-enumeration bound (where p is the smallest prime dividing the order of the group) has been the best worst-case result for general groups. In this work, we show the first improvement over the generator-enumeration bound for p-groups, which are believed to be the hard case of the group isomorphism problem. We… CONTINUE READING
    Beating the Generator-Enumeration Bound for Solvable-Group Isomorphism
    1
    On the Weisfeiler-Leman Dimension of Finite Groups
    Group Isomorphism with Fixed Subnormal Chains
    4
    Quantum Computation and Isomorphism Testing
    2
    Normalizers and permutational isomorphisms in simply-exponential time
    5

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 53 REFERENCES
    Breaking the nlog n Barrier for Solvable-Group Isomorphism
    13
    On the Complexity of Group Isomorphism
    7
    Code equivalence and group isomorphism
    44
    Linear time algorithms for Abelian group isomorphism and related problems
    32
    Testing isomorphism of combinatorial and algebraic structures
    14
    Polynomial-Time Isomorphism Test for Groups with No Abelian Normal Subgroups - (Extended Abstract)
    24
    Isomorphism of Graphs of Bounded Valence Can Be Tested in Polynomial Time
    • E. Luks
    • Mathematics, Computer Science
    • 1980
    234
    Polynomial-time Isomorphism Test for Groups with Abelian Sylow Towers
    21