General linear group:GL(2,Z9)
This article is about a particular group, i.e., a group unique upto isomorphism. View specific information (such as linear representation theory, subgroup structure) about this group
View a complete list of particular groups (this is a very huge list!)[SHOW MORE]
This group can be defined in the following equivalent ways:
- It is the group or , i.e., the general linear group of degree two over the ring of integers modulo .
- It is the group , i.e., the general linear group of degree two over the ring .
Note that although the rings in question are different, the corresponding general linear groups are isomorphic.
Want to compare and contrast arithmetic function values with other groups of the same order? Check out groups of order 3888#Arithmetic functions
Basic arithmetic functions
|order (number of elements, equivalently, cardinality or size of underlying set)||3888||groups with same order||As , a discrete valuation ring of length with residue field of size :|
|exponent of a group||72||groups with same order and exponent of a group | groups with same exponent of a group|
|nilpotency class||--||not a nilpotent group|
|derived length||4||groups with same order and derived length | groups with same derived length|
|GL(2,ZmodnZ(9))||GL and ZmodnZ|