Zeta functions of finite groups by enumerating subgroups

    Research output: Contribution to journalArticle


    For a finite group G, we consider the zeta function (Formula presented.), where H runs over the subgroups of G. First we give simple examples of abelian p-group G and non-abelian p-group G of order pm, m≥3 for odd p (resp. 2m, m≥4) for which (Formula presented.). Hence we see there are many non-abelian groups whose zeta functions have symmetry and Euler product, like the case of abelian groups. On the other hand, we show that ζG(s) determines the isomorphism class of G within abelian groups, by estimating the number of subgroups of abelian p-groups. Finally we study the problem which abelian p-group is associated with a non-abelian group having the same zeta function.

    Original languageEnglish
    Pages (from-to)1-12
    Number of pages12
    JournalCommunications in Algebra
    Publication statusAccepted/In press - 2017 Jan 7


    • Enumerating subgroups of abelian p-groups
    • enumerating subgroups of finite groups
    • local densities of square matrices
    • zeta functions of finite groups

    ASJC Scopus subject areas

    • Algebra and Number Theory

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