A generalized Baumslag–Solitar group (a GBS group) is a finitely generated group G acting on a tree so that all vertex and edge stabilizers are infinite cyclic groups. Each GBS group is the fundamental group π1(A) of some labeled graph A. We describe the centralizers of elements and the centralizer lattice. Also, we find the centralizer dimension for GBS groups if A is a labeled tree.
- centralizer dimension
- centralizer lattice
- generalized Baumslag–Solitar group
- generalized Baumslag-Solitar group