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dc.contributor.authorLooney, Carl Edwarden_US
dc.date.accessioned2015-12-11T23:20:06Z
dc.date.available2015-12-11T23:20:06Z
dc.date.submittedJanuary 2015en_US
dc.identifier.otherDISS-13286en_US
dc.identifier.urihttp://hdl.handle.net/10106/25360
dc.description.abstractIn 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.sponsorshipCordero, Minervaen_US
dc.language.isoenen_US
dc.publisherMathematicsen_US
dc.titleOn M-inverse Loops And Quasigroups Of Order N With A Long Inverse Cycle.en_US
dc.typePh.D.en_US
dc.contributor.committeeChairCordero, Minervaen_US
dc.degree.departmentMathematicsen_US
dc.degree.disciplineMathematicsen_US
dc.degree.grantorUniversity of Texas at Arlingtonen_US
dc.degree.leveldoctoralen_US
dc.degree.namePh.D.en_US


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