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.
","abstract_html":"<p>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.</p>","abstract_has_math":false,"creators":["Britten, Riley"],"institution":null,"degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Michael Kinyon","Petr Vojtechovsky","Maciej Kumosa","Nick Galatos"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-01-01T08:00:00Z","date_published":"2022-01-01T08:00:00Z","updated_at":"2026-07-24T02:02:03Z","subjects":["Moufang loops","Algebraic Geometry","Mathematics"],"languages":["en"],"rights":["Copyright is held by the author. User is responsible for all copyright compliance.
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"],"dc:subject":["Moufang loops","Algebraic Geometry","Mathematics"],"dc:title":["Topics in Moufang Loops"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-24T02:02:03Z"}