A regular group action of a group 
on a nonempty set 
is a group action such that,
for every pair of points 
, there is exactly one group
element 
such that 
. Equivalently, a regular group action is a group
action that is transitive and has trivial stabilizers.
A regular group action is also called a simply transitive group action or sharply
transitive group action.
Regular Group Action
See also
1-Arc-Regular Graph, Group Action, Group Orbit, Semiregular Group Action, Stabilizer, Transitive Group ActionExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Regular Group Action." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RegularGroupAction.html