EQUATIONS IN NILPOTENT GROUPS

作者：Duchin Moon^*; Liang Hao; Shapiro Michael

来源：PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2015, 143(11): 4723-4731.

DOI：10.1090/proc/12630

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.

• 出版日期2015-11