Originally Posted by

**Sudharaka** Hello,

If A={1,a,a^2,a^3,a^5} is a set defined under a binary operation * can this be considered as a cyclic group.

Since a^4 is not in the set A,I have concluded that,a*(a^3)=a^4 is not in the set A. And therefore * is not a binary operation,hence this is not a group.

Is this conclution correct.Therefore in my mind a cyclic group must contain all the powers of the generator(without missing powers inbetween) i.e: The set A should be {1,a,a^2,a^3,a^4,a^5} in order to call a cyclic group under *.

Are these things I have assumed correct?

Please answer my question as quick as you can.

Thank you.