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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
Rights Information: Copyright 2011 Jason Walter Elliot
Date Available in IDEALS: 2011-05-25
Date Deposited: 2011-05

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