On the isotopic characterizations of generalized Bol loops
Author
Adeniran, John Olusola
Jaiyeola, Temitope Gbolahan
Idowu, Kehinde Adisa
Full text
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/458110.22199/issn.0717-6279-4581
Abstract
In this study, the notion of isotopy of generalized Bol loop is characterized. A loop isotope of a σ-generalized Bol loop is shown to be a σ'-generalized Bol loop if σ' fixes its (isotope) identity element where σ' is some conjugate of σ. A loop isotope of a σ-generalized Bol loop is shown to be a σ'-generalized Bol loop if and only if the image of the isotope’s identity element under σ' is right nuclear (where σ' is some conjugate of σ). It is shown that a generalized Bol loop can be constructed using a group and a subgroup of it. A right conjugacy closed σ-generalized Bol loop is shown to be a σ-generalized right central loop.