Date of Award

Spring 2012

Degree Name

Bachelor of Science

Major

Mathematics

First Advisor

Melanie Stein

Abstract

The Lamplighter Group is an Algebraic Group whose behavior models the dynamics of a geometric system. In this thesis, a survey paper following a set of notes as written by Professor Jennifer Taback of Bowdoin College, we define this geometric system and the connection to the Lamplighter Group. Several subsequent results are then proven regarding word length of elements in the group and behavior within its Cayley Graph. A preliminary section is included to introduce the reader to several topics including Free Groups, Group Presentation, and the properties of the Cayley Graph.

Comments

Senior thesis completed at Trinity College for the degree of Bachelor of Science in Mathematics.

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