Group action refers to a way in which a group (or mathematical group) can systematically operate on a set, illustrating how the elements of the group can interact with the elements of the set. This concept is crucial in understanding symmetries and transformations, as it allows one to study the properties of sets by examining how groups manipulate them. Group actions help reveal structural aspects of both groups and sets, leading to insights about orbits, stabilizers, and the overall relationship between algebra and geometry.
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