: Matemáticas: profinite group

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profinite group

In mathematics, a profinite group is a topological group that is in a certain sense assembled from a system of finite groups. The idea of using a profinite group is to provide a "uniform", or "synoptic", view of an entire system of finite groups. Properties of the profinite group are generally speaking uniform properties of the system. For example, the profinite group is finitely generated (as a topological group) if and only if there exists ${\\displaystyle d\\in \\mathbb {N} }$ such that every group in the system can be generated by d elements. Many theorems about finite groups can be readily generalised to profinite groups; examples are Lagrange's theorem and the Sylow theorems.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Profinite_group)

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