Multiply set-transitive group action

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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


Symbol-free definition

A group action on a set is termed k-set-transitive or k-homogeneous for k \ge 1 if the following is true for all 1 \le l \le k:

Consider the natural action of the group on the set of subsets of size l. This action is a transitive group action.

A group action is termed multiply set-transitive or multiply homogeneous if it is k-set-transitive for some k > 1.

If a group action is k-set-transitive but not (k+1)-set-transitive, it is said to be sharply k-set-transitive.


Relation with other properties

Stronger properties