Growth in higher Baumslag–Solitar groups

Ayla P. Sánchez, Michael Shapiro

Research output: Contribution to journalArticlepeer-review

2 Citations (SciVal)


We study the HNN extension of (Formula presented.) given by the cubing endomorphism (Formula presented.), and prove that such groups have rational growth with respect to the standard generating sets. We compute the subgroup growth series of the horocyclic subgroup (Formula presented.) in this family of examples, prove that for each m the subgroup has rational growth. We then use the tree-like structure of these groups to see how to compute the growth of the whole group.

Original languageEnglish
Pages (from-to)1-21
Number of pages21
JournalGeometriae Dedicata
Early online date12 Aug 2017
Publication statusE-pub ahead of print - 12 Aug 2017


  • Baumslag–Solitar groups
  • Growth
  • Rationality
  • Solvable groups

ASJC Scopus subject areas

  • Geometry and Topology


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