Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $G$ be a finite group of order $n$. Prove that $G$ is cyclic if and only if $G$ contains an element of order $n$.

share|improve this question

closed as off-topic by Jonas Meyer, Krish, අරුණ, John, Najib Idrissi Mar 26 at 8:01

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Jonas Meyer, Krish, අරුණ, John, Najib Idrissi
If this question can be reworded to fit the rules in the help center, please edit the question.

Which part is giving you trouble, "if" or "only if"? –  Robert Israel Sep 13 '11 at 18:47
This question does not show any research effort –  The Chaz 2.0 Sep 13 '11 at 19:09
if and only if is obviously wrong. –  Dinesh Sep 13 '11 at 19:57
@Dinesh: Which part do you think is wrong? –  Robert Israel Sep 13 '11 at 20:11
@Dinesh, did you overlook $G$ is of order $n$? –  Soarer Sep 13 '11 at 20:29

1 Answer 1

The key component in the proof is that if $a^i=a^j$ for some element $a$ then $a^{i-j}=e$ and hence the order of $a$ divides $i-j$. To say more will be simply to write a complete solution of the question for you.

share|improve this answer

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