As commented here [1], the following two methods can be used to define an
Cyclic Group:
```
Generators
If the group operation is multiplication then:
<r | r ^ n =1>
If the group operation is addition then:
<z | n * z = 0 >
```
For the first case, the corresponding code snippet in GAP is as follows:
```
gap> f:=FreeGroup("P");;
gap> g:=f/ParseRelators(f, "P^8" );
<fp group on the generators [ P ]>
gap> StructureDescription(g);
"C8"
```
But I'm not sure if GAP also supports the second method mentioned above to
define a group.
[1]
http://www.euclideanspace.com/maths/discrete/groups/categorise/types/abelian/cyclic/index.htm
Regards,
HZ
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