| Autor: |
GIDEON OKON EFFIONG, JAIYÉOLÁ, TÈMÍTÓPÉ GBÓLÁHÀN, OBI, MARTIN CHUCKS, AKINOLA, LUKMAN SHINA |
| Předmět: |
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| Zdroj: |
Gulf Journal of Mathematics; 2024, Vol. 17 Issue 1, p142-166, 25p |
| Abstrakt: |
A loop (Q, ·) is called a Basarab loop if the identities: (x · yxρ) · (xz) = x · yz and (yx) · (xλz · x) = yz · x hold. The holomorphy of a Basarab loop Q was investigated with respect to a group A(Q) of automorphisms of the loop. Some necessary and sufficient conditions for an A(Q)-holomorph of a loop Q to be a left (right) Basarab loop or Basarab loop were established. Specifically, the A(Q)-holomorph of a loop Q was shown to be a left (right) Basarab loop if and only if Q is a left (right) Basarab loop and every element of A(Q) is left (right) regular. The A(Q)-holomorph of a loop Q was shown to be a Basarab loop if and only if Q is a Basarab loop, every element of A(Q) is both left and right nuclear and the A(Q)-generalized inner mappings of Q take some particular forms. These results were expressed in form of commutative diagrams. In any left (right) Basarab loop or Basarab loop Q, it was shown that the set of α ∈ A(Q) with four autotopic characterizations actually form normal subgroups of A(Q). [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
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