Classification of cyclic braces

91 citations recorded by the source corpus.

How researchers see this paper

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

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].”
Classification of braces of order p3 (2014, unknown): “(G, ·) ∼= { M3(3), p = 3 M(p), p 6= 3 11”
Solutions of the Yang-Baxter equation associated with a left brace (2015, methodology): “Fortunately, the complete classification of all the left brace structures with cyclic additive group of order p is known [24].”
Problems on skew left braces (2018, methodology): “Finite skew left braces with cyclic additive groups were classified by Rump in [61, 57].”
Braces and the Yang–Baxter Equation (2012, background): “Rump in [34] constructed finite multipermutation solutions of the YangBaxter equation of arbitrary multipermutation level such that their associated IYB groups are abelian.”
On skew braces (with an appendix by N. Byott and L. Vendramin) (2017, background): “Semidirect products of classical braces were considered by Rump [46].”
Extensions, matched products, and simple braces (2015, background): “Rump in [17] introduced a new algebraic structure called brace to study this class of solutions.”