Cyclic normal subgroups of generalized Baumslag-Solitar groups

The centers and cyclic radicals of generalized Baumslag-Solitar groups (GBS-groups) are studied. Criteria for their non-triviality are found and an algorithm to compute the center and cyclic radical,is given. In addition, for each unimodular GBS-group, a GBS-cover, i.e., a GBS-group in whose underlying graph the weights around each vertex are constant in absolute value, is, constructed. These groups are then characterized by a minimality property.