Classification of braces of order p3

By D. Bachiller. 2014

75 citations recorded by the source corpus.

A classification up to isomorphism of all left braces of order p3, where p is any prime number, is given. To this end, we first classify all the left braces of order p and p2, and then we construct explicitly the hypothesis required in [1, Corollary D] to build multiplications of left braces.

Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/c3657dbe1741a58907bc8e0518fbfe6b2cb89c5d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Leandro Vendramin
2. Ferran Cedó
3. Eric Jespers
4. D. Bachiller

In Discrete Mathematics and Combinatorics

1. Leandro Vendramin
2. Ferran Cedó
3. Eric Jespers
4. Jan Okninski
5. D. Bachiller
6. Tatiana Gateva-Ivanova
7. Agata Smoktunowicz

In Electrical and Electronic Engineering

1. Leandro Vendramin
2. Ferran Cedó
3. Eric Jespers

Citations in the corpus

• Iterated matched products of finite braces and simplicity; new solutions of the Yang-Baxter equation (2016, background): “Some partial results on the classification of “small” left braces can be found in [1, 23, 32].”
• Problems on skew left braces (2018, background): “Left braces of size p(2) and p(3), where p is a prime number, were classified by Bachiller in [3].”
• Bi-skew braces and Hopf Galois structures (2019, unknown): “2 of Bachiller’s classification of left braces in [2].”