Growth and cogrowth of normal subgroups of a free group

Johannes Jaerisch, Katsuhiko Matsuzaki

    Research output: Contribution to journalArticle

    Abstract

    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
    Volume145
    Issue number10
    DOIs
    Publication statusPublished - 2017 Jan 1

    Fingerprint

    Normal subgroup
    Free Group
    Quotient Graph
    Tend
    Planarity
    Lower bound
    Upper bound
    Sufficient Conditions

    Keywords

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

    ASJC Scopus subject areas

    • Mathematics(all)
    • Applied Mathematics

    Cite this

    Growth and cogrowth of normal subgroups of a free group. / Jaerisch, Johannes; Matsuzaki, Katsuhiko.

    In: Proceedings of the American Mathematical Society, Vol. 145, No. 10, 01.01.2017, p. 4141-4149.

    Research output: Contribution to journalArticle

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