String numbers of abelian groups

Anna Giordano Bruno, Simone Virili

    Research output: Contribution to journalArticleResearchpeer-review

    3 Citations (Scopus)


    The string number of self-maps arose in the context of algebraic entropy and it can be viewed as a kind of combinatorial entropy function. Later on, its values for endomorphisms of abelian groups were calculated in full generality. We study its global version for abelian groups, providing several examples involving also Hopfian abelian groups. Moreover, we characterize the class of all abelian groups with string number zero in many cases and discuss its stability properties. © 2012 World Scientific Publishing Company.
    Original languageEnglish
    Article number1250161
    JournalJournal of Algebra and Its Applications
    Issue number4
    Publication statusPublished - 1 Aug 2012


    • Abelian group
    • endomorphisms
    • hereditarily Hopfian group
    • Hopfian group
    • string numbers


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