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

Definition

A group action on a set is termed transitive if given any two elements of the set, there is a group element that takes the first element to the second.

By the fundamental theorem of group actions, any transitive group action on a nonempty set can be identified with the action on the coset space of the isotropy subgroup at some point.