The Parallel Complexity of Abelian Permutation Group Problems

@article{McKenzie1987ThePC,
  title={The Parallel Complexity of Abelian Permutation Group Problems},
  author={P. McKenzie and S. Cook},
  journal={SIAM J. Comput.},
  year={1987},
  volume={16},
  pages={880-909}
}
We classify Abelian permutation group problems with respect to their parallel complexity. For such groups specified by generating permutations we show that testing membership, computing order and testing isomorphism are $NC^1 $-equivalent to (and therefore have essentially the same parallel complexity as) determining solvability of a system of linear equations modulo a product of small prime powers; we show that intersecting two such groups is $NC^1 $-equivalent to computing setwise stabilizers… Expand
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