Central extensions of divisible groups

This thesis contributes to the classification of central extensions of divisible groups with finite abelian quotient, so called ``d-ab extensions.'' We give a matrix classification of equivalence classes of d-ab extensions and explicitly provide a family of group presentations. We provide a criterion for determining when two d-ab extensions are isomorophic in the case when the quotient is homocyclic. When the kernel has rank 1, we parametrize isomorphism classes of d-ab extensions with homocyclic quotient by constructing a family of group presentations. We also give a general reduction of d-ab extensions to the case when the kernel and center of the extensions coincide. For this case we give a classification of isomorphism classes when the kernel has rank 1. We highlight the applications of central extensions of divisible groups to nilpotent groups.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Elliot, Jason W.

Contributors dc:contributor

• Robinson, Derek J.S.
• Mineyev, Igor
• Ivanov, Sergei V.
• Ullom, Stephen V.

• divisible groups
• central extensions
• nilpotent groups
• group extensions

Statement dc:rights

• Copyright 2011 Jason Walter Elliot

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/24095

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/24095