Schreier groups and symmetric neighborhoods with a finite number of open components

Author

Raymond David Phillippi

Date of Award

5-2003

Degree Type

Thesis

Degree Name

Master of Science

Major

Mathematics

Major Professor

Conrad Plaut

Abstract

The purpose of this investigation is to consider the group structure of Schreier groups for both general topological groups and euclidean space in particular where U is taken to have a finite number of components. Theorem 1 exibits a homomorphism from the Schreier group into the direct product of the underlying topological group and a specified finitely presented group with the components of U as generators. Theorem 2 shows that in euclidean space the given homomorphism is an isomorphism. Examples are given which illustrate the process laid out in Theorem 1.

Recommended Citation

Phillippi, Raymond David, "Schreier groups and symmetric neighborhoods with a finite number of open components. " Master's Thesis, University of Tennessee, 2003.
https://trace.tennessee.edu/utk_gradthes/5278