Elementary abelian group of prime-square order
From Groupprops
Definition
Let be a prime number. We define the group
as the elementary abelian group whose order is
. We define it as the external direct product of two copies of the group of prime order
.
Arithmetic functions
GAP implementation
Group ID
This finite group has order p^2 and has ID 2 among the group of order p^2 in GAP's SmallGroup library. It can thus be defined using GAP's SmallGroup function as:
SmallGroup(p^2,2)
For instance, we can use the following assignment in GAP to create the group and name it :
gap> G := SmallGroup(p^2,2);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [p^2,2]
or just do:
IdGroup(G)
to have GAP output the group ID, that we can then compare to what we want.