Semigroup intersection problems in the Heisenberg groups

  title={Semigroup intersection problems in the Heisenberg groups},
  author={Rui-Tao Dong},
We consider two algorithmic problems concerning sub-semigroups of Heisenberg groups and, more generally, two-step nilpotent groups. The first problem is Intersection Emptiness , which asks whether a finite number of given finitely generated semigroups have empty intersection. This problem was first studied by Markov in the 1940s. We show that Intersection Emptiness is PTIME decidable in the Heisenberg groups H n ( K ) over any algebraic number field K , as well as in direct products of Heisenberg… 

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