University of Illinois Urbana-Champaign

Central extensions of divisible groups

Elliot, Jason W.

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Elliot_Jason.pdf

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

Description

Title
Central extensions of divisible groups
Author(s)
Elliot, Jason W.
Issue Date
2011-05-25T14:59:49Z
Director of Research (if dissertation) or Advisor (if thesis)
Robinson, Derek J.S.
Doctoral Committee Chair(s)
Mineyev, Igor
Committee Member(s)
  • Robinson, Derek J.S.
  • Ivanov, Sergei V.
  • Ullom, Stephen V.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Date of Ingest
2011-05-25T14:59:49Z
Keyword(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.
Graduation Semester
2011-05
Permalink
http://hdl.handle.net/2142/24095
Copyright and License Information
Copyright 2011 Jason Walter Elliot

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