Poorly connected groups

David Hume*, John M Mackay*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

1 Citation (Scopus)
36 Downloads (Pure)


We investigate groups whose Cayley graphs have poorly connected subgraphs. We prove that a finitely generated group has bounded separation in the sense of Benjamini–Schramm–Tim´ar if and only if it is virtually free. We then prove a gap theorem for connectivity of finitely presented groups, and prove that there is no comparable theorem for all finitely generated groups. Finally, we formulate a connectivity version of the conjecture that every group of type F with no Baumslag-Solitar subgroup is hyperbolic, and prove it for groups with at most quadratic Dehn function.
Original languageEnglish
Pages (from-to)4653-4664
JournalProceedings of the American Mathematical Society
Volume148 (2020)
Publication statusPublished - 14 Aug 2020


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