2-regular group action

This article defines a group action property or a property of group actions: a property that can be evaluated for a group acting on a set.
View a complete list of group action properties|Get help on group action property lookup|Get exploration suggestions
VIEW RELATED: group action property implications | group action property non-implications | {{{context space}}} metaproperty satisfactions | group action metaproperty dissatisfactions | group action property satisfactions |group action property dissatisfactions

Definition

Let $G$ be a group and $S$ be a set with a group action of $G$ on $S$. The action is 2-regular if the following is true: for any $a\neq b\in S$ and any $c\neq d\in S$, there is a unique $g\in G$ such that $g\cdot a=c,g\cdot b=d$.

Facts

• 2-regular group action implies elementary Abelian regular normal subgroup