Completion-equivalent subgroups

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]

For its use outside the wiki, please define the term when using it. If you are aware of an equivalent standard term, please leave a comment on the talk page
VIEW: Definitions built on this | Facts about this: (facts closely related to Completion-equivalent subgroups, all facts related to Completion-equivalent subgroups) |Survey articles about this | Survey articles about definitions built on this
VIEW RELATED: Analogues of this | Variations of this | Opposites of this |
Learn more about terminology local to the wiki | view a complete list of such terminology

Definition

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 $U$, $HU=G\iff KU=G$.