Date of Award

2022

Document Type

Dissertation

Degree Name

Ph.D.

Organizational Unit

College of Natural Science and Mathematics, Mathematics

First Advisor

Michael Kinyon

Second Advisor

Petr Vojtechovsky

Third Advisor

Maciej Kumosa

Fourth Advisor

Nick Galatos

Keywords

Moufang loops

Abstract

We will begin by discussing power graphs of Moufang loops. We are able to show that as in groups the directed power graph of a Moufang loop is uniquely determined by the undirected power graph. In the process of proving this result we define the generalized octonion loops, a variety of Moufang loops which behave analogously to the generalized quaternion groups. We proceed to investigate para-F quasigroups, a variety of quasigroups which we show are antilinear over Moufang loops. We briefly depart from the context of Moufang loops to discuss solvability in general loops. We then prove some results on the cosets of subloops of Moufang loops. Finally, we investigate generalizations of the variety of Moufang loops, the varieties of universally and semi-universally flexible loops.

Publication Statement

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

Rights Holder

Riley Britten

Provenance

Received from ProQuest

File Format

application/pdf

Language

en

File Size

123 pgs

Discipline

Mathematics

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