What is it about?
Holomorphy of Osborn loops is essentially an investigation of the conditions under which a holomorph of an Osborn loop will be an Osborn loop. In 1946 Bruck showed that a holomorph of a loop is a loop, since then researchers have been interested in examining the conditions for a holomorph of a particular loop to be that loop. Thus, this article outlines the conditions that allow a holomorph of Osborn loops to be Osborn.
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Why is it important?
Holomorphy of a loop is an upgrade of the loop. Especially when criptographic keys are found with the loop. Over time an upgrade will become necessary to further strengthen or fortify the keys or the system from hackers. At this time, refreshing the whole process with the loop's holomorph will serve to protect the system again, since a holomorph of the loop is actually the loop itself, by the inclusion of the conditions of the holomorphy.
Perspectives
Osborn loops are loops that do not allow some rules or properties that make computations easy. Thus, the work "holomorphy of Osborn loops"is a celebrated effort and a real contribution to loop theory.
Dr. Abednego O. Isere
Ambrose Alli University, Ekpoma
Read the Original
This page is a summary of: Holomorphy of Osborn loops, Annals of West University of Timisoara - Mathematics and Computer Science, January 2015, De Gruyter,
DOI: 10.1515/awutm-2015-0016.
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