# 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}
}```
• Published 1987
• Mathematics, Computer Science
• SIAM J. Comput.
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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