Volume 33 • Number 2 • 2010   • Weak Potency of Fundamental Groups of Graphs of Groups P. C. Wong, C. K. Tang and H. W. Gan Abstract. 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. 2000 Mathematics Subject Classification: Primary: 20E06, 20E26 20E08; Secondary: 20F05. Full text: PDF