Half-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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Definition

A group action on a set is termed half-transitive if given any two elements of the set, the size of their orbit is the same.

By the fundamental theorem of group actions, this means that their respective stabilizers have the same index in the group. Special cases occurs when the action is semiregular or transitive.