Highly 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

Symbol-free definition

A group action is termed highly transitive if it is $k$-transitive (in the sense of a multiply transitive group action) for every positive integer $k$.

Relation with other properties

Weaker properties

• Highly set-transitive group action
• Triply transitive group action
• Doubly transitive group action
• Primitive group action
• Transitive group action