On the Centralizer Dimension and Lattice of Generalized Baumslag–Solitar Groups

Аннотация

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.