English

Low-complexity computations for nilpotent subgroup problems

Group Theory 2017-07-05 v2

Abstract

We solve the following algorithmic problems using TC0 circuits, or in logspace and quasilinear time, uniformly in the class of nilpotent groups with bounded nilpotency class and rank: subgroup conjugacy, computing the normalizer and isolator of a subgroup, coset intersection, and computing the torsion subgroup. Additionally, if any input words are provided in compressed form as straight-line programs or in Mal'cev coordinates the algorithms run in quartic time.

Keywords

Cite

@article{arxiv.1706.01092,
  title  = {Low-complexity computations for nilpotent subgroup problems},
  author = {Jeremy Macdonald and Alexei Miasnikov and Denis Ovchinnikov},
  journal= {arXiv preprint arXiv:1706.01092},
  year   = {2017}
}

Comments

Updated to include TC0 results. 23 pages

R2 v1 2026-06-22T20:08:38.704Z