Weak potency of fundamental groups of graphs of groups - Wong, P.C.; Tang, C.K.; Gan, H.W. (Malaysian Mathematical Sciences Soc, 2010)
In this note we shall prove a characterization for the fundamental group of a graph of polycyclic-by-finite groups and free-by-finite groups with infinite cyclic edge subgroups to be weakly potent. We shall show also that all one-relator groups with non-trivial center are weakly potent.