Extensions, matched products, and simple braces

David Bachiller

    Research output: Contribution to journalArticleResearchpeer-review

    20 Citations (Scopus)


    © 2017 Elsevier B.V. We show how to construct all the extensions of left braces by ideals with trivial structure. This is useful to find new examples of left braces. But, to do so, we must know the basic blocks for extensions: the left braces with no ideals besides the trivial and the total ideal, called simple left braces. In this article, we present the first non-trivial examples of finite simple left braces. To explicitly construct them, we define the matched product of two left braces, which is a useful method to recover a finite left brace from its Sylow subgroups.
    Original languageEnglish
    Pages (from-to)1670-1691
    JournalJournal of Pure and Applied Algebra
    Issue number7
    Publication statusPublished - 1 Jul 2018


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