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arXiv · 1706.01092

Low-complexity computations for nilpotent subgroup problems

Jeremy Macdonald·Alexei Miasnikov·Denis Ovchinnikov
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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.

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Jeremy Macdonald, Alexei Miasnikov, Denis Ovchinnikov. 2017-06-04. Low-complexity computations for nilpotent subgroup problems. https://arxiv.org/abs/1706.01092

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