Direct product of Z8 and Z2
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This group, denoted or , can be defined in the following equivalent ways:
- It is the external direct product of the cyclic group of order eight (denoted or ) and the cyclic group of order two (denoted or ).
- It is the unique abelian group (up to isomorphism) of order sixteen and exponent eight.
Want to compare and contrast arithmetic function values with other groups of the same order? Check out groups of order 16#Arithmetic functions
|elementary abelian group||No|
This finite group has order 16 and has ID 5 among the groups of order 16 in GAP's SmallGroup library. For context, there are 14 groups of order 16. 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(16,5);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [16,5]
or just do:
to have GAP output the group ID, that we can then compare to what we want.
It can also be defined using GAP's DirectProduct function: