Geodesic
Crypto-automorphism group of some quasigroups
Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 1, pp. 57-72

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In quasigroup and loop theory, a pseudo-automorphism (with single companion) is known to generalize automorphism. In this work, the set of crypto-automorphisms (with twin companion) of a quasigroup with right and left identity elements were shown to form a group. For a quasigroup with right and left identity elements, some results on autotopic characterizations of crypto-automorphisms were established and used to deduce some subgroups of the crypto-automorphism group of a middle Bol loop. The crypto-automorphism group and Bryant-Schneider group (this has been used in the study of the isotopy-isomorphy of some varieties of loops e.g. Bol loops, Moufang loops, Osborn loops) of a loop were found to coincide.
Keywords: quasigroup, loop, crypto-automorphism, Bryant-Schneider group 
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Oyebo, Yakub Tunde; Osoba, Benard; Jaiyeola, Temitope Gbolahan. Crypto-automorphism group of some quasigroups. Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 1, pp. 57-72. http://geodesic.mathdoc.fr/item/DMGAA_2024_44_1_a3/