Home U+2200 to U+22FF Mathematical Operators

# U+22B3Contains As Normal Subgroup

U+22B3 was added to Unicode in version 1.1 (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 not a composition. It has a Neutral East Asian Width. In bidirectional context it acts as Other Neutral and is mirrored. Its corresponding mirrored glyph is Normal Subgroup Of. The glyph can, under circumstances, be confused with 1 other glyphs. In text U+22B3 behaves as Alphabetic regarding line breaks. It has type Other for sentence and Other for word breaks. The Grapheme Cluster Break is Any.

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 {displaystyle N} of the group G {displaystyle G} is normal in G {displaystyle G} if and only if g n g − 1 ∈ N {displaystyle gng^{-1}in N} for all g ∈ G {displaystyle gin G} and n ∈ N . {displaystyle nin N.} The usual notation for this relation is N ◃ G . {displaystyle N riangleleft 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 {displaystyle G} are precisely the kernels of group homomorphisms with domain G , {displaystyle 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
8883
UTF-8 E2 8A B3
UTF-16 22 B3
UTF-32 00 00 22 B3
URL-Quoted %E2%8A%B3
HTML-Escape &#x22B3;
Wrong windows-1252 Mojibake âŠ³
HTML-Escape &RightTriangle;
HTML-Escape &vartriangleright;
HTML-Escape &vrtri;
LATEX \vartriangleright

## Complete Record

Property Value
Age 1.1 (1993)
Unicode Name CONTAINS AS NORMAL SUBGROUP
Unicode 1 Name
Block Mathematical Operators
General Category Math Symbol
Script Common
Bidirectional Category Other Neutral
Combining Class Not Reordered
Decomposition Type None
Decomposition Mapping Contains As Normal Subgroup
Lowercase
Simple Lowercase Mapping Contains As Normal Subgroup
Lowercase Mapping Contains As Normal Subgroup
Uppercase
Simple Uppercase Mapping Contains As Normal Subgroup
Uppercase Mapping Contains As Normal Subgroup
Simple Titlecase Mapping Contains As Normal Subgroup
Titlecase Mapping Contains As Normal Subgroup
Case Folding Contains As Normal Subgroup
ASCII Hex Digit
Alphabetic
Bidi Control
Bidi Mirrored
Composition Exclusion
Case Ignorable
Changes When Casefolded
Changes When Casemapped
Changes When NFKC Casefolded
Changes When Lowercased
Changes When Titlecased
Changes When Uppercased
Cased
Full Composition Exclusion
Default Ignorable Code Point
Dash
Deprecated
Diacritic
Emoji Modifier Base
Emoji Component
Emoji Modifier
Emoji Presentation
Emoji
Extender
Extended Pictographic
FC NFKC Closure Contains As Normal Subgroup
Grapheme Cluster Break Any
Grapheme Base
Grapheme Extend
Hex Digit
Hyphen
ID Continue
ID Start
IDS Binary Operator
IDS Trinary Operator and
Ideographic
Indic Mantra Category
Indic Positional Category NA
Indic Syllabic Category Other
Jamo Short Name
Join Control
Logical Order Exception
Math
Noncharacter Code Point
NFC Quick Check Yes
NFD Quick Check Yes
NFKC Casefold Contains As Normal Subgroup
NFKC Quick Check Yes
NFKD Quick Check Yes
Other Alphabetic
Other Default Ignorable Code Point
Other Grapheme Extend
Other ID Continue
Other ID Start
Other Lowercase
Other Math
Other Uppercase
Prepended Concatenation Mark
Pattern Syntax
Pattern White Space
Quotation Mark
Regional Indicator
Sentence Break Other
Soft Dotted
Sentence Terminal
Terminal Punctuation
Unified Ideograph
Variation Selector
Word Break Other
White Space
XID Continue
XID Start
Expands On NFC
Expands On NFD
Expands On NFKC
Expands On NFKD
Bidi Mirrored Glyph Normal Subgroup Of
Bidi Paired Bracket Contains As Normal Subgroup
Bidi Paired Bracket Type None
East Asian Width Neutral
Hangul Syllable Type Not Applicable
ISO 10646 Comment
Joining Group No_Joining_Group
Joining Type Non Joining
Line Break Alphabetic
Numeric Type None
Numeric Value not a number
Simple Case Folding Contains As Normal Subgroup
Script Extension
Vertical Orientation R