U+2240 Wreath Product
U+2240 was added in Unicode version 1.1 in 1993. It belongs to the block
This character is a Math Symbol and is commonly used, that is, in no specific script.
The glyph is not a composition. It has no designated width in East Asian texts. In bidirectional text it acts as Other Neutral. When changing direction it is mirrored. The word that U+2240 forms with similar adjacent characters prevents a line break inside it.
The Wikipedia has the following information about this codepoint:
In group theory, the wreath product is a special combination of two groups based on the semidirect product. It is formed by the action of one group on many copies of another group, somewhat analogous to exponentiation. Wreath products are used in the classification of permutation groups and also provide a way of constructing interesting examples of groups.
Given two groups and (sometimes known as the bottom and top), there exist two variants of the wreath product: the unrestricted wreath product and the restricted wreath product . The general form, denoted by or respectively, requires that acts on some set ; when unspecified, usually (a regular wreath product), though a different is sometimes implied. The two variants coincide when , , and are all finite. Either variant is also denoted as (with wr for the LaTeX symbol) or A ≀ H (Unicode U+2240).
The notion generalizes to semigroups and, as such, is a central construction in the Krohn–Rhodes structure theory of finite semigroups.
Representations
System | Representation |
---|---|
Nº | 8768 |
UTF-8 | E2 89 80 |
UTF-16 | 22 40 |
UTF-32 | 00 00 22 40 |
URL-Quoted | %E2%89%80 |
HTML hex reference | ≀ |
Wrong windows-1252 Mojibake | ≀ |
HTML named entity | ≀ |
HTML named entity | ≀ |
HTML named entity | ≀ |
Encoding: GB18030 (hex bytes) | 81 36 D5 38 |
LATEX | \wr |
Elsewhere
Complete Record
Property | Value |
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1.1 (1993) | |
WREATH PRODUCT | |
— | |
Mathematical Operators | |
Math Symbol | |
Common | |
Other Neutral | |
Not Reordered | |
none | |
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✘ | |
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✘ | |
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✘ | |
✘ | |
✘ | |
✔ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
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Any | |
✔ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
0 | |
0 | |
0 | |
✘ | |
None | |
— | |
NA | |
Other | |
— | |
✘ | |
✘ | |
✘ | |
✔ | |
✘ | |
Yes | |
Yes | |
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Yes | |
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Yes | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✔ | |
✘ | |
✘ | |
✘ | |
✘ | |
Other | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
Other | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
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None | |
neutral | |
Not Applicable | |
— | |
No_Joining_Group | |
Non Joining | |
Alphabetic | |
none | |
not a number | |
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R |