Direct product of cyclic group of prime-square order and elementary abelian group of prime-square 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.
This group is defined in the following equivalent ways:
- : The external direct product of the cyclic group of prime-square order and the elementary abelian group of prime-square order.
- : The external direct product of the cyclic group of prime-square order and two copies of the cyclic group of prime order.
This group is thus the abelian group of prime power order corresponding to the partition (see also structure theorem for finitely generated abelian groups):
|Value of prime number||Corresponding group|
|2||direct product of Z4 and V4|
|3||direct product of Z9 and E9|
For instance, we can use the following assignment in GAP to create the group and name it :
gap> G := SmallGroup(p^4,11);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [p^4,11]
or just do:
to have GAP output the group ID, that we can then compare to what we want.
The exception is the case , in which case the group is .