Find the subgroups of
Z18
Z35
Z36
hint #1: any subgroup of a cyclic group is cyclic. so look at <k>, where k is an element of Zn.
hint #2: to avoid "duplicates" investigate the relationship between |k| and gcd(k,n).
hint #3: there will be only one subgroup of any given order (if you do what i ask in hint #2, you might be able to figure out "why" this is true).
hint #4: lagrange's theorem. use it.
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hint #1: any subgroup of a cyclic group is cyclic. so look at <k>, where k is an element of Zn.
hint #2: to avoid "duplicates" investigate the relationship between |k| and gcd(k,n).
hint #3: there will be only one subgroup of any given order (if you do what i ask in hint #2, you might be able to figure out "why" this is true).
hint #4: lagrange's theorem. use it.