Beating the Generator-Enumeration Bound for Solvable-Group Isomorphism

@article{Rosenbaum2020BeatingTG,
title={Beating the Generator-Enumeration Bound for Solvable-Group Isomorphism},
author={David J. Rosenbaum},
journal={ACM Transactions on Computation Theory (TOCT)},
year={2020},
volume={12},
pages={1 - 18}
}

We consider the isomorphism problem for groups specified by their multiplication tables. Until recently, the best published bound for the worst-case was achieved by the nlogp n + O(1) generator-enumeration algorithm where n is the order of the group and p is the smallest prime divisor of n. In previous work with Fabian Wagner, we showed an n(1 / 2) logp n + O(log n / log log n) -time algorithm for testing isomorphism of p-groups by building graphs with degree bounded by p + O(1) that represent… Expand