Finitely presented extensions by free groups
Gilbert Baumslag, Charles F Miller
JOURNAL OF GROUP THEORY | WALTER DE GRUYTER GMBH | Published : 2007
We prove here that a finitely presented group with a free quotient of rank n is an HNN-extension with n stable letters of a finitely generated group where the associated subgroups are finitely generated. This theorem has a number of consequences. In particular, in the event that the free quotient is cyclic it reduces to an elementary and quick proof of a theorem of Bieri and Strebel. © Walter de Gruyter 2007.