Algebraic group interpretations of dihedral group:D8
This article gives specific information, namely, algebraic group interpretations, about a particular group, namely: dihedral group:D8.
View algebraic group interpretations of particular groups | View other specific information about dihedral group:D8
Unitriangular matrix group interpretation
The group dihedral group:D8 can be interpreted as the group of -points of a unipotent algebraic group over the algebraic closure of , namely the unitriangular matrix group of degree three . Explicitly, , which in turn is the set of -fixed points of .
This is the only possible structure for as the -fixed points of a unipotent algebraic group.
|Field extension of field:F2||Degree of extension||Size of field||Size of group = cube of size of field||Group of points over that field in|
|field:F4||2||4||64||unitriangular matrix group:UT(3,4)|
|field:F8||3||8||512||unitriangular matrix group:UT(3,8)|
Local rings with this as residue field
|Local ring||Length of ring||Size of ring||Size of group = cube of size of ring||Corresponding algebraic group type notion|
|ring:Z4||2||4||64||unitriangular matrix group:UT(3,Z4)|
|2||4||64||unitriangular matrix group of degree three over quotient of polynomial ring over F2 by square of indeterminate|
|ring:Z8||3||8||512||unitriangular matrix group:UT(3,Z8)|