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Title:Central extensions of divisible groups
Author(s):Elliot, Jason W.
Director of Research:Robinson, Derek J.S.
Doctoral Committee Chair(s):Mineyev, Igor
Doctoral Committee Member(s):Robinson, Derek J.S.; Ivanov, Sergei V.; Ullom, Stephen V.
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):divisible groups
central extensions
nilpotent groups
group extensions
Abstract: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.
Issue Date:2011-05-25
URI:http://hdl.handle.net/2142/24095
Rights Information:Copyright 2011 Jason Walter Elliot
Date Available in IDEALS:2011-05-25
Date Deposited:2011-05


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