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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)

Abstract

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.

Keywords

Word Problem Cayley Graph Wreath Product Membership Problem Metabelian Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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