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# U+22EDDoes Not Contain As Normal Subgroup Or Equal

U+22ED was added in Unicode version 1.1 in 1993. It belongs to the block U+2200 to U+22FF Mathematical Operators in the U+0000 to U+FFFF Basic Multilingual Plane.

This character is a Math Symbol and is commonly used, that is, in no specific script.

The glyph is a canonical composition of the glyphs Contains As Normal Subgroup Or Equal To, Combining Long Solidus Overlay. It has no designated width in East Asian texts. In bidirectional text it acts as Other Neutral. When changing direction it is mirrored into Not Normal Subgroup of Or Equal To. The word that U+22ED forms with similar adjacent characters prevents a line break inside it.

The CLDR project calls this character “does not contain as normal subgroup equal” for use in screen reading software. It assigns these additional labels, e.g. for search in emoji pickers: group theory, mathematics.

In abstract algebra, a normal subgroup (also known as an invariant subgroup or self-conjugate subgroup) is a subgroup that is invariant under conjugation by members of the group of which it is a part. In other words, a subgroup $N$ of the group $G$ is normal in $G$ if and only if $gn{g}^{-1}\in N$ for all $g\in G$ and $n\in N.$ The usual notation for this relation is $N◃G.$

Normal subgroups are important because they (and only they) can be used to construct quotient groups of the given group. Furthermore, the normal subgroups of $G$ are precisely the kernels of group homomorphisms with domain $G,$ which means that they can be used to internally classify those homomorphisms.

Évariste Galois was the first to realize the importance of the existence of normal subgroups.

## Representations

System Representation
8941
UTF-16 22 ED
UTF-32 00 00 22 ED
HTML hex reference &#x22ED;
Wrong windows-1252 Mojibake â‹­
HTML named entity &NotRightTriangleEqual;
HTML named entity &nrtrie;
HTML named entity &ntrianglerighteq;
LATEX \ntrianglerighteq

## Complete Record

Property Value
Age (age) 1.1 (1993)
Unicode Name (na) DOES NOT CONTAIN AS NORMAL SUBGROUP OR EQUAL
Unicode 1 Name (na1)
Block (blk) Mathematical Operators
General Category (gc) Math Symbol
Script (sc) Common
Bidirectional Category (bc) Other Neutral
Combining Class (ccc) Not Reordered
Decomposition Type (dt) canonical
Decomposition Mapping (dm) Contains As Normal Subgroup Or Equal To Combining Long Solidus Overlay
Lowercase (Lower)
Simple Lowercase Mapping (slc) Does Not Contain As Normal Subgroup Or Equal
Lowercase Mapping (lc) Does Not Contain As Normal Subgroup Or Equal
Uppercase (Upper)
Simple Uppercase Mapping (suc) Does Not Contain As Normal Subgroup Or Equal
Uppercase Mapping (uc) Does Not Contain As Normal Subgroup Or Equal
Simple Titlecase Mapping (stc) Does Not Contain As Normal Subgroup Or Equal
Titlecase Mapping (tc) Does Not Contain As Normal Subgroup Or Equal
Case Folding (cf) Does Not Contain As Normal Subgroup Or Equal
ASCII Hex Digit (AHex)
Alphabetic (Alpha)
Bidi Control (Bidi_C)
Bidi Mirrored (Bidi_M)
Composition Exclusion (CE)
Case Ignorable (CI)
Changes When Casefolded (CWCF)
Changes When Casemapped (CWCM)
Changes When NFKC Casefolded (CWKCF)
Changes When Lowercased (CWL)
Changes When Titlecased (CWT)
Changes When Uppercased (CWU)
Cased (Cased)
Full Composition Exclusion (Comp_Ex)
Default Ignorable Code Point (DI)
Dash (Dash)
Deprecated (Dep)
Diacritic (Dia)
Emoji Modifier Base (EBase)
Emoji Component (EComp)
Emoji Modifier (EMod)
Emoji Presentation (EPres)
Emoji (Emoji)
Extender (Ext)
Extended Pictographic (ExtPict)
FC NFKC Closure (FC_NFKC) Does Not Contain As Normal Subgroup Or Equal
Grapheme Cluster Break (GCB) Any
Grapheme Base (Gr_Base)
Grapheme Extend (Gr_Ext)
Hex Digit (Hex)
Hyphen (Hyphen)
ID Continue (IDC)
ID Start (IDS)
IDS Binary Operator (IDSB)
IDS Trinary Operator and (IDST)
IDSU (IDSU) 0
ID_Compat_Math_Continue (ID_Compat_Math_Continue) 0
ID_Compat_Math_Start (ID_Compat_Math_Start) 0
Ideographic (Ideo)
InCB (InCB) None
Indic Mantra Category (InMC)
Indic Positional Category (InPC) NA
Indic Syllabic Category (InSC) Other
Jamo Short Name (JSN)
Join Control (Join_C)
Logical Order Exception (LOE)
Math (Math)
Noncharacter Code Point (NChar)
NFC Quick Check (NFC_QC) Yes
NFD Quick Check (NFD_QC) No
NFKC Casefold (NFKC_CF) Does Not Contain As Normal Subgroup Or Equal
NFKC Quick Check (NFKC_QC) Yes
NFKC_SCF (NFKC_SCF) Does Not Contain As Normal Subgroup Or Equal
NFKD Quick Check (NFKD_QC) No
Other Alphabetic (OAlpha)
Other Default Ignorable Code Point (ODI)
Other Grapheme Extend (OGr_Ext)
Other ID Continue (OIDC)
Other ID Start (OIDS)
Other Lowercase (OLower)
Other Math (OMath)
Other Uppercase (OUpper)
Prepended Concatenation Mark (PCM)
Pattern Syntax (Pat_Syn)
Pattern White Space (Pat_WS)
Quotation Mark (QMark)
Regional Indicator (RI)
Sentence Break (SB) Other
Soft Dotted (SD)
Sentence Terminal (STerm)
Terminal Punctuation (Term)
Unified Ideograph (UIdeo)
Variation Selector (VS)
Word Break (WB) Other
White Space (WSpace)
XID Continue (XIDC)
XID Start (XIDS)
Expands On NFC (XO_NFC)
Expands On NFD (XO_NFD)
Expands On NFKC (XO_NFKC)
Expands On NFKD (XO_NFKD)
Bidi Mirrored Glyph (bmg) Not Normal Subgroup of Or Equal To
Bidi Paired Bracket (bpb) Does Not Contain As Normal Subgroup Or Equal
Bidi Paired Bracket Type (bpt) None
East Asian Width (ea) neutral
Hangul Syllable Type (hst) Not Applicable
ISO 10646 Comment (isc)
Joining Group (jg) No_Joining_Group
Joining Type (jt) Non Joining
Line Break (lb) Alphabetic
Numeric Type (nt) none
Numeric Value (nv) not a number
Simple Case Folding (scf) Does Not Contain As Normal Subgroup Or Equal
Script Extension (scx)
Vertical Orientation (vo) R