Identificador persistente para citar o vincular este elemento:
http://hdl.handle.net/10662/16373
Títulos: | On a class of power associative LCC-loops |
Autores/as: | George, O.O. Olaleru, J.O. Adéníran, J.O. Jaiyéolá, T.G |
Palabras clave: | Lazo cerrado de conjugación izquierda (derecha);Asociatividad de potencia;Lazo LWPC;Lazo RWPC;Left (right) conjugacy closed loop,;Power associativity;LWPC-loop;RWPC-loop |
Fecha de publicación: | 2022 |
Editor/a: | Universidad de Extremadura, Servicio de Publicaciones |
Resumen: | Let LWPC denote the identity (xy · x) · xz = x((yx · x)z), and RWPC the mirror identity. Phillips proved that a loop satisfies LWPC and RWPC if and only if it is a WIP PACC loop. Here, it is proved that a loop Q fulfils LWPC if and only if it is a left conjugacy closed (LCC) loop that fulfils the identity (xy · x)x = x(yx · x). Similarly, RWPC is equivalent to RCC and x(x · yx) = (x · xy)x. If a loop satisfies LWPC or RWPC, then it is power associative (PA). The smallest nonassociative LWPC-loop was found to be unique and of order 6 while there are exactly 6 nonassociative LWPC-loops of order 8 up to isomorphism. Methods of construction of nonassociative LWPC-loops were developed. |
URI: | http://hdl.handle.net/10662/16373 |
ISSN: | 0213-8743 |
DOI: | 10.17398/2605-5686.37.2.185 |
Colección: | Extracta Mathematicae Vol. 37, nº 2 (2022) |
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