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group action

/ɡruːp ˈækʃən/ · group·ac·tion
noun
  1. A formal way in which a mathematical group operates on a set, assigning to each group element a transformation of the set that respects the group operation. The symmetric group S₃ acts on the set {1,2,3} by permuting its elements, providing a classic example of a group action.

Synonyms

group operationgroup representationgroup homomorphismpermutation actionsymmetry actionorbit actionaction of a groupgroup action
Did you know? Group actions underpin the solution of the Rubik's Cube, where the cube's twists form a group that acts on the set of its colored stickers.

Related terms

group (mathematics)setpermutationorbitstabilizerhomomorphism
Written by Lexi Wordsworth, Dictionary Editor 0 lookups Added Aug 19, 2026