On the Baumslag -Solitar groups and certain generalized free products.

Title: On the Baumslag -Solitar groups and certain generalized free products.
Identifier: AAI3232014
identifier: 3232014
Creator: Clement, Anthony E.
Contributor: Adviser: Gilbert Baumslag
Date: 2006
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: The class of the Baumslag groups G(m,n) yields examples of finitely generated 1-relator groups that fail to be residually finite [7]. With the utilization of "the Magnus breakdown" of 1-relator groups, in conjunction with the Reidemeister-Schreier method, our analysis of the structure of the groups G(m,n) exhibits, as subgroups, the class of the Baumslag-Solitar groups B(m,n).;In 1991 D.I. Moldavanskii [24] gave a complete solution to the isomorphism problem for the class of the Baumslag-Solitar groups. This thesis takes a different approach to the problem of pairwise distinguishing the members of the class of the Baumslag-Solitar groups.;In 1966, S. Lipschutz [17] solved the conjugacy problem for the generalized free product of free groups with cyclic amalgam. In 1962, G. Baumslag [2] proved that a certain generalized free product G of free group F and free abelian group A with cyclic amalgam is residually free. Motivated by the desire to extend this result, we derived an algorithm for solving the conjugacy problem in a special case of this generalized free product G.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.

Media: On the Baumslag -Solitar groups and certain generalized free products.