Counterexample to a conjecture about braces

David Bachiller

Research output: Contribution to journalArticleResearchpeer-review

33 Citations (Scopus)


© 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 languageEnglish
Pages (from-to)160-176
JournalJournal of Algebra
Publication statusPublished - 1 May 2016


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

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