Countable primitive groups

Tsachik Gelander, Yair Glasner

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


We give a complete characterization of countable primitive groups in several settings including linear groups, subgroups of mapping class groups, groups acting minimally on trees and convergence groups. The latter category includes as a special case Kleinian groups as well as subgroups of word hyperbolic groups. As an application we calculate the Frattini subgroup in many of these settings, often generalizing results that were only known for finitely generated groups. In particular, we answer a question of G. Higman and B.H. Neumann on the Frattini group of an amalgamated product.

Original languageEnglish
Pages (from-to)1479-1523
Number of pages45
JournalGeometric and Functional Analysis
Issue number5
StatePublished - 1 Jan 2008


  • Frattini subgroups
  • Hyperbolic groups
  • Linear groups
  • Mapping class groups
  • Maximal subgroups
  • Permutation groups
  • Primitive actions

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology


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