\(\mathcal {F}_\pi \)-residuality of generalized Baumslag–Solitar groups

  • F.A. DudkinEmail author


A generalized Baumslag–Solitar group is a finitely generated group that acts on a tree with infinite cyclic edge and vertex stabilizers. A group G is residually a finite \(\pi \)-group, for a set of primes \(\pi \), if every non-trivial element of G has non-trivial image in a quotient of G that is a finite \(\pi \)-group. We provide a criterion for generalized Baumslag–Solitar groups to be residually a finite \(\pi \)-group.


Residual \(\pi \)-finiteness Residual finiteness Generalized Baumslag–Solitar group Baumslag–Solitar group 

Mathematics Subject Classification

20E06 20E08 



The work was supported by Russian Science Foundation (project 19-11-00039).


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Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

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