On certain isotopic maps of central loops

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 of pseudoautomorphisms and right translations of elements 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.