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 π-group, for a set of primes π, if every non-trivial element of G has non-trivial image in a quotient of G that is a finite π-group. We provide a criterion for generalized Baumslag–Solitar groups to be residually a finite π-group.
- Baumslag–Solitar group
- Generalized Baumslag–Solitar group
- Residual finiteness
- Residual π-finiteness
- 1.01 MATHEMATICS