What is it about?
In quasigroup and loop theory, a pseudo-automorphism (with single com panion) 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 characteri zations 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.
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Why is it important?
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.
Perspectives
Looking for subgroups of the crypto-automorphism group of a middle Bol loop? This article will help out. Do you know that the crypto-automorphism group and Bryant-Schneider group of a loop coincide? yes!
Professor Temitope Gbolahan Jaiyeola
Obafemi Awolowo University
Read the Original
This page is a summary of: Crypto-automorphism group of some quasigroups, Discussiones Mathematicae - General Algebra and Applications, January 2024, Uniwersytet Zielonogórski,
DOI: 10.7151/dmgaa.1433.
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