Elementary abelian group:E9
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This elementary abelian group is defined in the following equivalent ways:
- It is the elementary abelian group of prime-square order where the prime is three.
- It is the additive group of the field of nine elements.
- It is a direct product of two copies of the cyclic group of order three.
Want to compare and contrast arithmetic function values with other groups of the same order? Check out groups of order 9#Arithmetic functions
|elementary abelian group||Yes|
This finite group has order 9 and has ID 2 among the groups of order 9 in GAP's SmallGroup library. For context, there are groups of order 9. 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(9,2);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [9,2]
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: