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This group, denoted , is defined as the cyclic group of order .
|elementary abelian group||No|
|group of prime power order||Yes|
This finite group has order 9 and has ID 1 among the groups of order 9 in GAP's SmallGroup library. For context, there are groups of order 9. It can thus be defined using GAP's SmallGroup function as:
For instance, we can use the following assignment in GAP to create the group and name it :
gap> G := SmallGroup(9,1);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [9,1]
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: