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In 1966, F. Rhodes introduced the idea of the fundamental group of a group acting on a topological space. His article contains summarized proofs of results and has been studied since then primarily because the category of transformation groups is more general than the category of topological spaces. In this article, a thorough study of Rhodes’s work is presented, providing examples to enrich the theory. Dr. James Montaldi from the University of Manchester has recently provided a more general and applicable approach Rhodes’s main theorem. His results are also analyzed here.

El Grupo Fundamental de un Grupo que Actúa en un Espacio Topológico