Generously transitive 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.
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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

This is a variation of transitivity|Find other variations of transitivity |

Definition

Symbol-free definition

A group action on a set is termed generously transitive if given any two elements in the set, there is an element of the group that acts to interchange the two elements.

Definition with symbols

A group action of a group $G$ on a set $S$ is termed generously transitive if given any two elements $a$ and $b$ in $S$ , there is a $g$ in $G$ such that $g.a=b$ and $g.b=a$ .