I want someone to check my proof Suppose the cyclic group with one generator can have more than 2 element Consider 2 element since number of generator can't exceed number of element then it has 2 element. But if it not,It must have <1> as generator and atleast

prime number as generator.That contradict Therefore cyclic group with only one generator can have at most 2 element


Take $G$ such a Group with its unique generator $g\in G$. But then $g^n=e\iff \left(g^{-1}\right)^n=e$ thus $g^{-1}$ is also a generator. Can you take from here?

  • $\begingroup$ I can't . I have I just started read abstract algebra I'm newbie in this field-*- $\endgroup$ – Lingnoi401 Nov 1 '16 at 6:20
  • $\begingroup$ ok I get that now thank $\endgroup$ – Lingnoi401 Nov 1 '16 at 6:21

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.