#
nLab

transitive action

# Contents

## Definition

An action

$\rho : G \times X \to X$

of a group $G$ on a set $X$ is *transitive* if for every $x \in X$ the morphisms

$\rho_x : G \to X$

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

Revised on November 30, 2011 21:42:40
by

Zoran Škoda
(161.53.130.104)