Growth and cogrowth of normal subgroups of a free group

Johannes Jaerisch, Katsuhiko Matsuzaki

    Research output: Contribution to journalArticle

    1 Citation (Scopus)


    We give a sufficient condition for a sequence of normal subgroups of a free group to have the property that both their growths tend to the upper bound and their cogrowths tend to the lower bound. The condition is represented by planarity of the quotient graphs of the tree.

    Original languageEnglish
    Pages (from-to)4141-4149
    Number of pages9
    JournalProceedings of the American Mathematical Society
    Issue number10
    Publication statusPublished - 2017 Jan 1


    • Bottom of spectrum
    • Cogrowth
    • Discrete Laplacian
    • Growth tight
    • Isoperimetric constant
    • Planar graph
    • Poincaré exponent

    ASJC Scopus subject areas

    • Mathematics(all)
    • Applied Mathematics

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