New Identities In Universal Osborn Loops

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dc.creatorJaiyeola, Temitope Gbolahan
dc.creatorAdeniran, John Olusola
dc.date2009-05-13
dc.date.accessioned2026-07-07T13:14:27Z
dc.date.available2026-07-07T13:14:27Z
dc.descriptionA question associated with the 2005 open problem of Michael Kinyon (Is every Osborn loop universal?), is answered. Two nice identities that characterize universal (left and right universal) Osborn loops are established. Numerous new identities are established for universal (left and right universal) Osborn loops like CC-loops, VD-loops and universal weak inverse property loops. Particularly, Moufang loops are discovered to obey the new identity $[y(x^{-1}u)\cdot u^{-1}](xu)=[y(xu)\cdot u^{-1}](x^{-1}u)$ surprisingly. For the first time, new loop properties that are weaker forms of well known loop properties like inverse property, power associativity and diassociativity are introduced and studied in universal (left and right universal) Osborn loops. Some of them are found to be necessary and sufficient conditions for a universal Osborn to be 3 power associative. For instance, four of them are found to be new necessary and sufficient conditions for a CC-loop to be power associative. A conjugacy closed loop is shown to be diassociative if and only if it is power associative and has a weak form of diassociativity.
dc.description22 pages
dc.identifierhttps://arxiv.org/abs/0905.2040
dc.identifierhttp://arxiv.org/abs/0905.2040
dc.identifierQuasigroups And Related Systems, Vol. 17, No. 1(2009), 55-76
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/230214
dc.subjectGeneral Mathematics
dc.subjectGroup Theory
dc.subject20NO5 ; 08A05
dc.titleNew Identities In Universal Osborn Loops
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