# 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.