Elementary abelian group of prime-cube order
This article is about a family of groups with a parameter that is prime. For any fixed value of the prime, we get a particular group.
View other such prime-parametrized groups
Let be a prime number. The elementary abelian group of order , denoted , is the elementary abelian group whose order is . In other words, it is (up to isomorphism) the external direct product of three copies of the group of prime order.
|Value of prime number||Corresponding group|
|2||elementary abelian group:E8|
|3||elementary abelian group:E27|
|5||elementary abelian group:E125|
|7||elementary abelian group:E343|
For instance, we can use the following assignment in GAP to create the group and name it :
gap> G := SmallGroup(p^3,5);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [p^3,5]
or just do:
to have GAP output the group ID, that we can then compare to what we want.
The group can also be defined using GAP's ElementaryAbelianGroup function: