English

Logspace and compressed-word computations in nilpotent groups

Group Theory 2021-12-21 v3 Computational Complexity

Abstract

For finitely generated nilpotent groups, we employ Mal'cev coordinates to solve several classical algorithmic problems efficiently. Computation of normal forms, the membership problem, the conjugacy problem, and computation of presentations for subgroups are solved using only logarithmic space and quasilinear time. Logarithmic space presentation-uniform versions of these algorithms are provided. Compressed-word versions of the same problems, in which each input word is provided as a straight-line program, are solved in polynomial time.

Keywords

Cite

@article{arxiv.1503.03888,
  title  = {Logspace and compressed-word computations in nilpotent groups},
  author = {Jeremy Macdonald and Alexei Myasnikov and Andrey Nikolaev and Svetla Vassileva},
  journal= {arXiv preprint arXiv:1503.03888},
  year   = {2021}
}

Comments

Accepted in Transactions of the AMS

R2 v1 2026-06-22T08:51:43.958Z