Peterzil-Steinhorn subgroups of Real Algebraic Groups

Doctoral Dissertation

Abstract

We consider Peterzil-Steinhorn groups defined in o-minimal expansions of the reals. These are one-dimensional torsion-free subgroups of arbitrary definable and not definably compact groups. We show that each Peterzil-Steinhorn group is isomorphic to either the additive or the multiplicative group of the reals and we provide a simple criterion that can be used to classify each such group into one of those two categories. Additionally, we find the tangent space of any arbitrary Peterzil-Steinhorn group at its identity. Finally, for the case of polynomially bounded o-minimal expansions of the reals, we give a complete description of all Peterzil-Steinhorn groups.

Attributes

Attribute NameValues
URN
  • etd-11302013-190602

Author Georgios Poulios
Advisor Sergei Starchenko
Contributor Liviu Nicolaescu, Committee Member
Contributor Vincent Guingona, Committee Member
Contributor Anand Pillay, Committee Member
Contributor Sergei Starchenko, Committee Chair
Degree Level Doctoral Dissertation
Degree Discipline Mathematics
Degree Name PhD
Defense Date
  • 2013-11-26

Submission Date 2013-11-30
Country
  • United States of America

Subject
  • mathematical logic

  • o-minimality

  • model theory

  • definable groups

Publisher
  • University of Notre Dame

Language
  • English

Record Visibility and Access Public
Content License
  • All rights reserved

Departments and Units

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