IA-automorphisms and localization of nilpotent groups.

Title: IA-automorphisms and localization of nilpotent groups.
Identifier: AAI3284392
identifier: 3284392
Creator: Zyman, Marcos.
Contributor: Adviser: Joseph Roitberg
Date: 2007
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: A group is called p-local, where p is a prime number, if every element in the group has a unique nth root for each n relatively prime to p. Given a nilpotent group G and a prime p, there is a unique p-local group G( p) which is, in some sense, the "best approximation" to G among all p-local nilpotent groups. G(p) is called the p-localization of G.;Let G(p ) be the p-localization of a nilpotent group G, and let IA(G) be the subgroup of AutG consisting of those automorphisms of G that induce the identity on G/G', where G' denotes the commutator subgroup of G. IA(G) turns out to be nilpotent, so its p-localization exists. Two groups G and H are said to be in the same localization genus if G( p) is isomorphic to H( p) for all primes p. The main result of this thesis is that if two finitely generated, torsion-free, nilpotent, and metabelian groups lie in the same localization genus, their IA -groups also lie in the same localization genus. The method of proof involves basic sequences and commutator calculus.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.