On certain isotopic maps of central loops
DOI:
https://doi.org/10.4067/S0716-09172011000300003Keywords:
Central loop, Isotopism, Autotopism, Bryant-Schneider group.Abstract
It is shown that the Holomorph of a C-loop is a C-loop if each element of the automorphism group of the loops is left nuclear. Condition under which an element of the Bryant-Schneider group of a C-loop will form an automorphism is established. It is proved that elements of the Bryant-Schneider group of a C-loop can be expressed a product ofpseudo-automorphisms and right translations ofelements of the nucleus of the loop. The Bryant-Schneider group of a C-loop is also shown to be a kind of generalized holomorph of the loop.
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