Non-commutative lattice problems
-
Alexei Myasnikov
,
Andrey Nikolaev
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 nontrivial 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.
Funding source: Russian Science Foundation
Award Identifier / Grant number: 14-11-00085
Funding source: NSF
Award Identifier / Grant number: DMS-1318716
Funding statement: The work on Section 3 was supported by Russian Science Foundation, project 14-11-00085. The work on the other sections was supported by NSF grant DMS-1318716.
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© 2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- Sliceable groups and towers of fields
- Pro-Hall R-groups and groups discriminated by the free pro-p group
- Filtrations of free groups arising from the lower central series
- Prosolvability criteria and properties of the prosolvable radical via Sylow sequences
- Non-commutative lattice problems
- Conjugacy distinguished subgroups
- Diophantine questions in the class of finitely generated nilpotent groups
- Uncountably many non-commensurable finitely presented pro-p groups
- Singer torus in irreducible representations of GL(n,q)
- Virtually free pro-p products
Articles in the same Issue
- Frontmatter
- Sliceable groups and towers of fields
- Pro-Hall R-groups and groups discriminated by the free pro-p group
- Filtrations of free groups arising from the lower central series
- Prosolvability criteria and properties of the prosolvable radical via Sylow sequences
- Non-commutative lattice problems
- Conjugacy distinguished subgroups
- Diophantine questions in the class of finitely generated nilpotent groups
- Uncountably many non-commensurable finitely presented pro-p groups
- Singer torus in irreducible representations of GL(n,q)
- Virtually free pro-p products
