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.
['Markus Lohrey', 'Benjamin Steinberg', 'Georg Zetzsche']
Rational subsets and submonoids of wreath products