On the isotopic characterizations of generalized Bol loops
DOI:
https://doi.org/10.22199/issn.0717-6279-4581Keywords:
Bol loops, generalized Bol loopsAbstract
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.
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