Geometric and Functional Analysis

, Volume 17, Issue 5, pp 1479–1523 | Cite as

Countable Primitive Groups

Article

Abstract.

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.

Keywords and phrases:

Permutation groups primitive actions maximal subgroups linear groups mapping class groups hyperbolic groups frattini subgroups 

AMS Mathematics Subject Classification:

Primary 20B15 Secondary 20B07, 20E28 

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Copyright information

© Birkhaeuser 2007

Authors and Affiliations

  1. 1.Institute of MathematicsThe Hebrew UniversityJerusalemIsrael
  2. 2.Department of MathematicsBen Gurion University of the NegevBe’er ShevaIsrael

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