2007•Journal of Group TheoryRequires access

Finitely presented extensions by free groups

Gilbert Baumslag, Charles F. Miller

Abstract

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.

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Key concepts: Mathematics, Quotient, Stallings theorem about ends of groups, Finitely-generated abelian group, Rank (graph theory), Free group, Finitely generated group, Extension (predicate logic)