Random nilpotent groups, polycyclic presentations, and Diophantine problems

DOI10.1515/gcc-2017-0007zbMath1378.20049arXiv1612.02651OpenAlexW2766154976MaRDI QIDQ1676247

Denis Ovchinnikov, Albert Garreta, Alexei G. Myasnikov

Publication date: 6 November 2017

Published in: Groups, Complexity, Cryptology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.02651

zbMATH Keywords

nilpotent groupspolycyclic groupsDiophantine problemrandom groups

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Nilpotent groups (20F18) Stochastic processes (60G99) Probabilistic methods in group theory (20P05)

Related Items

Metabelian groups: full-rank presentations, randomness and Diophantine problems ⋮ Parallel complexity for nilpotent groups ⋮ Random nilpotent groups, polycyclic presentations, and Diophantine problems ⋮ Full rank presentations and nilpotent groups: structure, Diophantine problem, and genericity ⋮ \(C^\ast\)-stability of discrete groups ⋮ Post's correspondence problem: from computer science to algebra ⋮ The Diophantine problem in some metabelian groups ⋮ Post's Correspondence Problem for hyperbolic and virtually nilpotent groups ⋮ Deciding isomorphy using Dehn fillings, the splitting case ⋮ TC^0 circuits for algorithmic problems in nilpotent groups ⋮ Low-complexity computations for nilpotent subgroup problems ⋮ Two general schemes of algebraic cryptography ⋮ Diophantine problems in solvable groups

Cites Work

• Random walk in random groups.
• Random nilpotent groups, polycyclic presentations, and Diophantine problems
• Equations in nilpotent groups
• Random Nilpotent Groups I
• A Matrix Model for Random Nilpotent Groups
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