Mathematics > Group Theory
[Submitted on 10 Jan 2014]
Title:Equations in nilpotent groups
View PDFAbstract: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.
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