### Abstract

© 2016 Elsevier Inc. We find an example of a finite solvable group (in fact, a finite p-group) in which is not possible to define a left brace structure or, equivalently, which is not an IYB group. This answers a question posed by Cedó, Jespers and del Río related to the Yang-Baxter equation. Our argument is an improvement of an argument of Rump, using results about Hopf-Galois extensions and LSA structures. We explain explicitly the relation between these two areas of mathematics and brace theory, hoping that it will be useful in the future.

Original language | English |
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Pages (from-to) | 160-176 |

Journal | Journal of Algebra |

Volume | 453 |

DOIs | |

Publication status | Published - 1 May 2016 |

### Keywords

- Bijective 1-cocycle
- Braces
- Hopf-Galois extensions
- IYB group
- Lie algebras
- LSA structures
- Nilpotent group
- Primary
- Radical rings
- Secondary

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## Cite this

Bachiller, D. (2016). Counterexample to a conjecture about braces.

*Journal of Algebra*,*453*, 160-176. https://doi.org/10.1016/j.jalgebra.2016.01.011