On the Bryant-Schneider Group of Right Cheban Loop
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Authors: A. I. CHINAKA, A. O. ABDULKAREEM, B. OSOBA, Y. T. OYEBO AND J. O. ADENIRAN
DOI: 10.46793/KgJMat2609.1413C
Abstract:
In this study, we investigate the Bryant-Schneider group of right Cheban loops. The study started with establishing some results on the algebraic properties of right Cheban loop. Consequently, it is established that every right pseudo-automorphism of a right Cheban loop is an element of the Bryant-Schneider group. It is shown that the middle inner mapping Ta is an automorphism of a right Cheban loop if and only if a ∈ Nμ of the right Cheban loop. Ra and La are subsequently shown to be elements of the Bryant-Schneider group. The Crypto-automorphism group of right Cheban loop is investigated. A two-middle pseudo-automorphism group, the crypto-automorphism group and the Bryant-Scheider group of a loop are found to coincide.
Keywords:
Bryant-Schneider group, crypto-automorphism group, pseudo-automorphism, right Cheban loop.
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