Question

Suppose G is a cyclic group and H be any subgroup of G. Which of the following statements is true?

a) H is abelian.


b) H is cyclic.


c) H is finitely generated.


d) All of the above.​

Answer 1

Answer:

If your cyclic group has order n, there will be one generator for every number between 1 and n1 (inclusive) that is relatively prime to n: in other words, there are phi(n) generators, where phi is Euler's totient function.