Central extensions of divisible groups

Elliot, Jason W.

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

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

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

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

Copyright and License Information

Copyright 2011 Jason Walter Elliot

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