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14: Group Actions

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    Group actions generalize group multiplication. If \(G\) is a group and \(X\) is an arbitrary set, a group action of an element \(g \in G\) and \(x \in X\) is a product, \(gx\text{,}\) living in \(X\text{.}\) Many problems in algebra are best be attacked via group actions. For example, the proofs of the Sylow theorems and of Burnside's Counting Theorem are most easily understood when they are formulated in terms of group actions.

    This page titled 14: Group Actions is shared under a GNU Free Documentation License 1.3 license and was authored, remixed, and/or curated by Thomas W. Judson (Abstract Algebra: Theory and Applications) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

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