Does Not Contain As Normal Subgroup

Does Not Contain As Normal Subgroup at U+22EB denotes the negation of a group-theory containment relation: the group on the right is not a normal subgroup of the group on the left. It is part of the Mathematical Operators block and is used as a specialized symbolic relation rather than as ordinary punctuation. Its real-world use is almost entirely in abstract algebra, especially finite group theory, ring and module analogies, and lecture notes that distinguish subgroup inclusion from normal subgroup inclusion. For example, an author may write G ⋫ N to state that N is contained in G but is not normal there, depending on the convention used in that text; the unnegated companion relation expresses “contains as a normal subgroup.” The symbol is most likely to appear in research papers, textbooks, theorem statements, and computer typeset mathematics where compact notation is preferred over a phrase such as “does not contain as a normal subgroup.” Because conventions around left-versus-right containment symbols can vary, readers should check the surrounding notation, especially when both subgroup and normal-subgroup relation signs appear in the same work.