On middle universal weak and cross inverse property loops with equal length of inverse cycles
This study presents a special type of middle isotopism under which the weak inverse property (WIP) is isotopic invariant in loops. A sufficient condition for a WIPL that is specially isotopic to a loop to be isomorphic to the loop isotope is established. It is shown that under this special type of m...
- Autores:
-
Temitope Gbolahan, Jaiyeola
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2010
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/39763
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/39763
http://bdigital.unal.edu.co/29860/
- Palabra clave:
- Cross inverse property loops (CIPLs)
Weak inverse property loops (WIPLs)
Inverse cycles
20NO5
08A05
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
Summary: | This study presents a special type of middle isotopism under which the weak inverse property (WIP) is isotopic invariant in loops. A sufficient condition for a WIPL that is specially isotopic to a loop to be isomorphic to the loop isotope is established. It is shown that under this special type of middle isotopism, whenever $n$ is a positive even integer, a finite WIPL has an inverse cycle of length $n$ if and only if its isotope is a finite WIPL with an inverse cycle of length $n$. But, when $n$ is an odd positive integer and a loop (or its isotope) is a finite WIPL with only $e$ and inverse cycles of length $n$, then its isotope (or the loop) is a finite WIPL with only $e$ and inverse cycles of length $n$ if and only if they are isomorphic. Hence, both are isomorphic CIPLs. Explanations and procedures are given on how these results can be used to apply CIPLs to cryptography. |
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