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## Abstract

This paper shows that every finite non-degenerate involutive set theoretic solution (X,r) of the Yang–Baxter equation whose permutation group G(X,r) has cardinality which is a cube-free number is a multipermutation solution. Some properties of finite braces are also investigated. It is also shown that if A is a left brace whose cardinality is an odd number and (−a)⋅b=−(a⋅b) for all a,b∈A, then A is a two-sided brace and hence a Jacobson radical ring. It is also observed that the semidirect product and the wreath product of braces of a finite multipermutation level is a brace of a finite multipermutation level.

Original language | English |
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Pages (from-to) | 3-18 |

Number of pages | 16 |

Journal | Journal of Algebra |

Volume | 500 |

Early online date | 6 May 2016 |

DOIs | |

Publication status | Published - 15 Apr 2018 |

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