nLab
transitive action

Contents

Definition

An action

ρ:G×XX \rho : G \times X \to X

of a group GG on a set XX is transitive if for every xXx \in X the morphisms

ρ x:GX \rho_x : G \to X

is an epimorphism, i.e. for every two points x,xx,x' there exists gGg\in G such that x=gxx' = g x.

Revised on November 30, 2011 21:42:40 by Zoran Škoda (161.53.130.104)