Direct product of Z9 and Z3
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Contents
Definition
This group is defined as the direct product of the cyclic group of order 9 and the cyclic group of order 3.
Arithmetic functions
GAP implementation
Group ID
This finite group has order 27 and has ID 2 among the groups of order 27 in GAP's SmallGroup library. For context, there are groups of order 27. It can thus be defined using GAP's SmallGroup function as:
SmallGroup(27,2)
For instance, we can use the following assignment in GAP to create the group and name it :
gap> G := SmallGroup(27,2);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [27,2]
or just do:
IdGroup(G)
to have GAP output the group ID, that we can then compare to what we want.
Other descriptions
The group can be constructed using GAP's DirectProduct and CyclicGroup functions:
DirectProduct(CyclicGroup(9),CyclicGroup(3))