Date of Award

6-1-2013

Document Type

Dissertation

Degree Name

Ph.D.

Organizational Unit

College of Natual Science and Mathematics

First Advisor

Michael K. Kinyon, Ph.D.

Second Advisor

Petr Vojtěchovský

Third Advisor

Nikolaos Galatos

Fourth Advisor

Lawrence Berliner

Abstract

This dissertation uses the connections between loops and their associated permutation groups to study certain varieties of loops. We first define a variety of loops generalizing commutative automorphic loops and show this new variety is power associative. We show a correspondence to Bruck loops of odd order and use this correspondence to give structural results for our new variety, which in turn hold for commutative automorphic loops. Next, we study a variety of loops that generalize both Moufang and Steiner loops. We extend on known results for Moufang loops and then extend two different doubling constructions for creating Moufang and other varieties of loops. We then give a general construction to create simple RCC loops from GL(2,q) for q a prime power. Finally, we consider a generalization of Bruck loops, and show that different companions of pseudoautomorphism live in certain subloops.

Publication Statement

Copyright is held by the author. User is responsible for all copyright compliance.

Rights Holder

Mark Greer

Provenance

Received from ProQuest

File Format

application/pdf

Language

en

File Size

129 p.

Discipline

Mathematics

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