@article{Jaiyéolá_Effiong_2021, title={Basarab loop and the generators of its total multiplication group}, volume={40}, url={https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4430}, DOI={10.22199/issn.0717-6279-2021-4430}, abstractNote={<p><em>A loop (Q; ·) is called a Basarab loop if the identities: (x · yx<sup>ρ</sup>)(xz) = x · yz and (yx) · (x<sup>λ</sup>z · x) = yz · x hold. It was shown that the left, right and middle nuclei of the Basarab loop coincide, and the nucleus of a Basarab loop is the set of elements x whose middle inner mapping T<sub>x</sub> are automorphisms. The generators of the inner mapping group of a Basarab loop were refined in terms of one of the generators of the total inner mapping group of a Basarab loop. Necessary and su_cient condition(s) in terms of the inner mapping group (associators) for a loop to be a Basarab loop were established. It was discovered that in a Basarab loop: the mapping x ↦ T<sub>x</sub> is an endomorphism if and only if the left (right) inner mapping is a left (right) regular mapping. It was established that a Basarab loop is a left and right automorphic loop and that the left and right inner mappings belong to its middle inner mapping group. A Basarab loop was shown to be an automorphic loop (A-loop) if and only if it is a middle automorphic loop (middle A-loop). Some interesting relations involving the generators of the total multiplication group and total inner mapping group of a Basarab loop were derived, and based on these, the generators of the total inner mapping group of a Basarab loop were finetuned. A Basarab loop was shown to be a totally automorphic loop (TA-loop) if and only if it is a commutative and exible loop. These aforementioned results were used to give a partial answer to a 2013 question and an ostensible solution to a 2015 problem in the case of Basarab loop</em></p>}, number={4}, journal={Proyecciones (Antofagasta, On line)}, author={Jaiyéolá, Temitope and Effiong, Gideon}, year={2021}, month={Jul.}, pages={939-962} }