dc.contributor.author | Looney, Carl Edward | en_US |
dc.date.accessioned | 2015-12-11T23:20:06Z | |
dc.date.available | 2015-12-11T23:20:06Z | |
dc.date.submitted | January 2015 | en_US |
dc.identifier.other | DISS-13286 | en_US |
dc.identifier.uri | http://hdl.handle.net/10106/25360 | |
dc.description.abstract | In 2002, A.D Keedwell and V.A Sherbacov introduced the concept of finite m-inverse quasigroups with long inverse cycles. Keedwell and Sherbacov observed that finite m-inverse loops and quasigroups with a long inverse cycle could be useful in the study of cryptology. Keedwell and Sherbacov studied the existence of these algebraic structures by determining if a Cayley table of the elements of such structures could be constructed. They showed that m-inverse loops of order 9 with a long inverse cycle do not exist for m = 2; 4 and 6; thus, there do not exist 2,4, or 6 inverse-quasigroups of order 8. However the investigation of 3 or 7-inverse loops of order 9 and of 3 or 7-inverse quasigroups of order 8 with a long inverse cycle was considered more complicated and was left unanswered. In this paper we attack the unanswered question of the existence of 3 and 7-inverse loops and quasigroups with long inverse cycles. We also investigate the following two problems: (i)The existence of m-inverse loops with a long inverse cycle of orders 11 and 15. (ii)The existence of m-inverse quasigroups with a long inverse cycle of order 12,16 and 20. | en_US |
dc.description.sponsorship | Cordero, Minerva | en_US |
dc.language.iso | en | en_US |
dc.publisher | Mathematics | en_US |
dc.title | On M-inverse Loops And Quasigroups Of Order N With A Long Inverse Cycle. | en_US |
dc.type | Ph.D. | en_US |
dc.contributor.committeeChair | Cordero, Minerva | en_US |
dc.degree.department | Mathematics | en_US |
dc.degree.discipline | Mathematics | en_US |
dc.degree.grantor | University of Texas at Arlington | en_US |
dc.degree.level | doctoral | en_US |
dc.degree.name | Ph.D. | en_US |