Cyclic 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
where is the identity element. The group is written or .
|Value of prime number||Corresponding group|
For instance, we can use the following assignment in GAP to create the group and name it :
gap> G := SmallGroup(p^3,1);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [p^3,1]
or just do:
to have GAP output the group ID, that we can then compare to what we want.
The group can be described using GAP's CyclicGroup function:
where we can replace by a particular prime or replace by a particular cube of a prime.