Steinberg symbol

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In algebra, the Hausdorff completion G^ of a group G with filtration Gn is the inverse limit limG/Gn of the discrete group G/Gn. A basic example is a profinite completion. The image of the canonical map GG^ is a Hausdorff topological group and its kernel is the intersection of all Gn: i.e., the closure of the identity element. The canonical homomorphism gr(G)gr(G^) is an isomorphism.

The concept is named after Felix Hausdorff.

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