Growth and cogrowth of normal subgroups of a free group

Johannes Jaerisch, Katsuhiko Matsuzaki

Research output: Contribution to journalArticlepeer-review

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


  • 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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