A group action is a formal way in which a group interacts with a set, where each element of the group corresponds to a function that transforms the set while preserving its structure. Essentially, it defines how the group's elements can 'act' on the elements of a set, providing a powerful framework for understanding symmetries and transformations in various mathematical contexts. This concept is key in connecting groups with geometric and topological structures, allowing us to study how these actions can influence the properties of spaces.
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