Cyclic groups (rows) and its subgroups
What does this matrix show:
In rows there is n. In cols there is k.
n means the order of cyclic group Zn.
k means the "jump" size.
The matrix shows "OK" when applying the jump k you are able to reach all elements of the group.
Nice conculsions:
Cyclic group Zn=12 has podgroups of size 2,3 and 4 but not 5.
Cyclic group Zn where n is a prime has no podgroups (all elements in row have OK)
Elements of cyclic group for n=12:
k-th element of cyclic group for k=5: