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arXiv · 1508.02388

Non-commutative lattice problems

Alexei Myasnikov·Andrey Nikolaev·Alexander Ushakov
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Abstract

We consider several subgroup-related algorithmic questions in groups, modeled after the classic computational lattice problems, and study their computational complexity. We find polynomial time solutions to problems like finding a subgroup element closest to a given group element, or finding a shortest non-trivial element of a subgroup in the case of nilpotent groups, and a large class of surface groups and Coxeter groups. We also provide polynomial time algorithm to compute geodesics in given generators of a subgroup of a free group.

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BibTeXRIS

Alexei Myasnikov, Andrey Nikolaev, Alexander Ushakov. 2015-08-10. Non-commutative lattice problems. https://arxiv.org/abs/1508.02388

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