Invariants of 1-relator groups and residual properties of amalgamated products.

Title: Invariants of 1-relator groups and residual properties of amalgamated products.
Identifier: AAI9530917
identifier: 9530917
Creator: Schneider, Elizabeth Ruth.
Contributor: Adviser: Gilbert Baumslag
Date: 1995
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: This work is concerned with properties of the lower central series of finitely generated 1-relator groups and amalgamated products. We prove that the torsion-free ranks of the lower central factors of a finitely generated 1-relator group depend only on the number of generators and the weight of the relator. In addition, we give several sets of necessary conditions for the amalgamated product of two {dollar}{lcub}\cal U{rcub}{dollar}-groups to be a {dollar}{lcub}\cal U{rcub}{dollar}-group, and prove that the amalgamated product of two finitely generated torsion-free nilpotent groups over an isolated cyclic subgroup is a residually finite p-group for almost all primes p. We also consider the amalgamated product of two free groups over an isolated cyclic subgroup, and exhibit a large class of cases in which such groups will be residually torsion-free nilpotent.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.

Media: Invariants of 1-relator groups and residual properties of amalgamated products.