Completion-equivalent subgroups

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This article defines an equivalence relation over the collection of subgroups within the same big group

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]


Definition with symbols

Let G be a group and H and K be subgroups of G. We say that H and K are completion-equivalent if for any subgroup U, HU = G \iff KU = G.