Galici, M., & Nagy, G. P. (2024). AN EXTENSION FORMULA FOR RIGHT BOL LOOPS ARISING FROM BOL REFLECTIONS. arXiv preprint arXiv:2410.09977v1.
This paper investigates a new extension formula for right Bol loops, aiming to determine the conditions under which the extension also results in a right Bol loop.
The authors utilize tools from both geometric and group theory. They leverage the concept of Bol reflections within the framework of 3-nets associated with loops. Additionally, they employ Aschbacher's Bol loop folder method, which connects loop structures to group-theoretic data.
The paper provides a novel construction method for right Bol loops, expanding the understanding of these algebraic structures. The authors establish necessary and sufficient conditions for the extension to inherit the right Bol property and explore the properties of the resulting loop, including its nuclei, center, and core.
This research contributes to the field of loop theory by introducing a new extension formula and analyzing its properties. The findings provide insights into the structure and behavior of right Bol loops, potentially leading to the discovery of new classes and applications of these algebraic structures.
The paper focuses on a specific extension formula for right Bol loops. Further research could explore other potential extension methods and their properties. Additionally, investigating the applications of these extended loops in areas such as cryptography and coding theory could be fruitful.
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by Mario Galici... at arxiv.org 10-15-2024
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