Elementary abelian group:E64
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This group is defined as the elementary abelian group of order , i.e., the direct product of six copies of the cyclic group of order two. It can also be viewed as the additive group of a six-dimensional vector space over the field of two elements.
As an abelian group of prime power order
This group is the abelian group of prime power order corresponding to the partition:
In other words, it is the group .
|Value of prime number||Corresponding group|
|generic prime||elementary abelian group of prime-sixth order|
|3||elementary abelian group:E729|
|5||elementary abelian group:E15625|
Want to compare and contrast arithmetic function values with other groups of the same order? Check out groups of order 64#Arithmetic functions
|elementary abelian group||Yes|
This finite group has order 64 and has ID 267 among the groups of order 64 in GAP's SmallGroup library. For context, there are groups of order 64. It can thus be defined using GAP's SmallGroup function as:
For instance, we can use the following assignment in GAP to create the group and name it :
gap> G := SmallGroup(64,267);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [64,267]
or just do:
to have GAP output the group ID, that we can then compare to what we want.
The group can be defined using GAP's ElementaryAbelianGroup function as: