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