Equations in nilpotent groups
Copyright policy )Equations in nilpotent groups
We show that there exists an algorithm to decide any single equation in the Heisenberg group in finite time. The method works for all two-step nilpotent groups with rank-one commutator, which includes the higher Heisenberg groups. We also prove that the decision problem for systems of equations is unsolvable in all non-abelian free nilpotent groups.
- Tufts University United States
Word problems, other decision problems, connections with logic and automata (group-theoretic aspects), nilpotent groups, Group Theory (math.GR), algorithms, Heisenberg group, equations over groups, Algebraic geometry over groups; equations over groups, Nilpotent groups, FOS: Mathematics, 20F10, 20F18, 20F70, Mathematics - Group Theory
Word problems, other decision problems, connections with logic and automata (group-theoretic aspects), nilpotent groups, Group Theory (math.GR), algorithms, Heisenberg group, equations over groups, Algebraic geometry over groups; equations over groups, Nilpotent groups, FOS: Mathematics, 20F10, 20F18, 20F70, Mathematics - Group Theory
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