Date of Award

1-1-2013

Document Type

Dissertation

Degree Name

Ph.D.

Department

Mathematics

First Advisor

Michael K. Kinyon

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.

Provenance

Recieved from ProQuest

Rights holder

Mark Benjamin Greer

File size

129 p.

File format

application/pdf

Language

en

Discipline

Mathematics

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