The Mathematical Symbol "Not Normal Subgroup Of (⋪)"

Delving into the "Not Normal Subgroup Of" Symbol (⋪)

The ⋪ symbol, often referenced in the realm of group theory in mathematics, stands for "Not Normal Subgroup Of." This article will dive into the symbol's meaning and showcase its use with various examples.

Meaning of ⋪

In abstract algebra, particularly in group theory, a normal subgroup is a subgroup that remains invariant under conjugation by any element of the group. The ⋪ symbol is used to indicate that a given subgroup is not a normal subgroup of another group.

Example 1: Basic Group Theory

If you have groups \( G \) and \( H \), and \( H \) is not a normal subgroup of \( G \), this can be represented as: \[ H ⋪ G \]

Example 2: Further Applications in Algebra

In some algebraic contexts, one might come across multiple subgroups and their relationships. If \( K \) and \( L \) are both not normal subgroups of \( G \), it can be expressed as: \[ K ⋪ G \] and \( L ⋪ G \]

Applications of ⋪

The ⋪ symbol has its primary application in:

  • Mathematics: Specifically in abstract algebra and group theory to represent non-normal subgroups.
  • Research: Scholars and researchers use this symbol in academic papers and publications dealing with group theory concepts.

To conclude, the ⋪ symbol plays a pivotal role in showing the relationships between groups and their subgroups in the context of abstract algebra. Familiarizing oneself with such symbols is vital for those studying advanced mathematics and algebra.

Mathematical symbol 'Not Normal Subgroup Of'

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Codes for the ⋪ Symbol

The Symbol
Alt CodeAlt 8938
HTML Code⋪
HTML Entity⋪
CSS Code\22EA
Hex Code⋪

How To Insert the ⋪ Symbol

(Method 1) Copy and paste the symbol.

The easiest way to get the ⋪ symbol is to copy and paste it into your document.

Bear in mind that this is a UTF-8 encoded character. It must be encoded as UTF-8 at all stages (copying, replacing, editing, pasting), otherwise it will render as random characters or the dreaded �.

(Method 2) Use the "Alt Code."

If you have a keyboard with a numeric pad, you can use this method. Simply hold down the Alt key and type 8938. When you lift the Alt key, the symbol appears. ("Num Lock" must be on.)

(Method 3) Use the HTML Decimal Code (for webpages).

HTML TextOutput
<b>My symbol: &#8938;</b>My symbol: ⋪

(Method 4) Use the HTML Entity Code (for webpages).

HTML TextOutput
<b>My symbol: &nltri;</b>My symbol: ⋪

(Method 5) Use the CSS Code (for webpages).

CSS and HTML TextOutput
span:after {
content: "\22EA";}
<span>My symbol:</span>
My symbol: ⋪

(Method 6) Use the HTML Hex Code (for webpages and HTML canvas).

HTML TextOutput
<b>My symbol: &#x22EA;</b>My symbol: ⋪
On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x22EA to place the ⋪ symbol on your canvas. For example:
JavaScript Text
const x = "0x"+"E9"
ctx.fillText(String.fromCodePoint(x), 5, 5);

(Method 7) Use the Unicode (for various, e.g. Microsoft Office, JavaScript, Perl).

The Unicode for ⋪ is U+22EA. The important part is the hexadecimal number after the U+, which is used in various formats. For example, in Microsoft Office applications (e.g. Word, PowerPoint), do the following:
[Hold down Alt]
[Press x]

(The 22EA turns into ⋪. Note that you can omit any leading zeros.)
In JavaScript, the syntax is \uXXXX. So, our example would be \u22EA. (Note that the format is 4 hexadecimal characters.)
JavaScript TextOutput
let str = "\u22EA"
document.write("My symbol: " + str)
My symbol: ⋪