👉 In mathematics, a "completions" is a concept that is used in order to study certain mathematical structures. A completion of a group G at an element x ∈ G means that every subgroup H of G which contains x as its center has a unique representative in G. This is often denoted by the notation G ∼_{x}H. For example, if G is a finite group and x is any non-trivial element of G, then the completion of G at x can
