Extensões de grupos finitamente apresentados por grupos livres

Abstract

Using the theory of ends, J. Stallings showed in 1971 that any finitely generated with infinitely many ends has a decomposition either as a non-trivial generalizated free product or as an HNN-extension where the amalgamated (respectively associated) sugbroups are finite. In 1972, Karrass, Pietrowiski e Solitar provide a caracterization for finite and cyclic extension of a free group and in 1978, R. Bieri and R. Strebel described an almost-finitely generated group over a ring as a HNN-extension with a single stable letter. The present work aims to provide a detailed proof to a result by G. Baumslag and C. F. Miller III that includes as a consequence, the results of Karrass and Bieri: Theorem: Let G be a finitely presented group with a free quocient of rank n. Then G is an HNN-extension with n stable letters, of a finitely generated groupo B finitely generated associated subgroups.