Regular 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

Definition

A regular group action of a group on a nonempty set is a group action that satisfies the following euqivalent conditions:

  1. It is both transitive and semiregular.
  2. For any two (possibly equal) elements of the set, there is a unique group element taking the first to the second.
  3. It is equivalent to the left-regular group action: the action of a group on itself by left multiplication.

Relation with other properties

Weaker properties

Related properties