Group action

Orbit

Given an action of a group on a set , the orbit¹ of a point is the set of points that may be mapped to when acted upon, i.e. group

It follows the restriction of an action onto an orbit is transitive, and the induced subgroup of is called the transitive constituent.

Properties

• Orbit cardinality divides the finite order of the group element
• Orbit-stabilizer theorem
• Since orbits partition , one can form an orbit space .
• Iff the action is said to be transitive.

See also

• Group action orbital, and the more general n-orbit.
• Group action suborbit

---

tidy | en | sembr

Footnotes

1. German Bahn ↩