Left braces of size 8p
Teresa Crespo, Daniel Gil-Mu\~noz, Anna Rio, Montserrat Vela
TL;DR
This paper classifies all left braces of size 8p for odd primes p not equal to 3 or 7, confirming previous counts and providing a detailed characterization of their isomorphism classes.
Contribution
It offers a complete classification of left braces of size 8p for certain primes, including a characterization of isomorphism classes and a method to derive braces from size 8 cases.
Findings
Validated the number of left braces of size 8p for specified primes.
Described conjugacy classes of regular subgroups related to braces.
Provided a characterization for isomorphism classes of semidirect product braces.
Abstract
We describe all left braces of size 8p for p an odd prime different from 3 or 7 and validate the number given by Bardakov, Neschadim and Yadav. We give a characterization for isomorphism classes of a semidirect product of left braces and then the description is done by first describing left braces of size 8, as conjugacy classes of regular subgroups of the corresponding holomorph, and then checking how many non isomorphic left braces of size 8p are obtained from each one of them.
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