Rational Subsets and Submonoids of Wreath Products

  • Markus Lohrey
  • Benjamin Steinberg
  • Georg Zetzsche
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7966)


It is shown that membership in rational subsets of wreath products H ≀ V with H a finite group and V a virtually free group is decidable. On the other hand, it is shown that there exists a fixed finitely generated submonoid in the wreath product ℤ ≀ ℤ with an undecidable membership problem.


Word Problem Cayley Graph Wreath Product Membership Problem Metabelian Group 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Markus Lohrey
    • 1
  • Benjamin Steinberg
    • 2
  • Georg Zetzsche
    • 3
  1. 1.Institut für InformatikUniversität LeipzigGermany
  2. 2.Department of MathematicsCity College of New YorkUSA
  3. 3.Fachbereich InformatikTechnische Universität KaiserslauternGermany

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