Physical Sciences and Mathematics Commons^™

Loops And Their Permutation Groups, Mark Greer

Electronic Theses and Dissertations

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 …