Residual solvability of generalized free products.

Title: Residual solvability of generalized free products.
Identifier: AAI3144106
identifier: 3144106
Creator: Kahrobaei, Delaram.
Contributor: Adviser: Gilbert Baumslag
Date: 2004
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: The notion of residual properties was first introduced by Philip Hall in 1954. In this work we show that in general G = {lcub}A * B; C{rcub}, the generalized product of two finitely generated nilpotent groups A and B, amalgamating C, is not perfect. As a consequence, when the factors A and B are torsion-free, G is guaranteed to be residually solvable by any of the following conditions: (1) the amalgamated subgroup C is central in both factors; (2) the amalgamated subgroup C is of finite index in at least one of the factors; (3) the factors A and B are isomorphic, via an isomorphism that agrees with the isomorphism that identifies the amalgamated subgroups CA and C B (this type of generalized free product is called a double); (4) the amalgamated subgroup C is cyclic; (5) one of the factors is abelian. The generalized free products of finitely generated torsion-free nilpotent groups are not necessarily residually solvable. We demonstrate that using an example due to Gilbert Baumslag.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.