The order of the group $G$, meet the following conditions: $1<G<n$ where n is a natural number.
For each 2 sub groups $H_1$, $H_2$ of $G$, if $H_1 \neq H_2$ then $\gcd(|H_1|,|H_2|)=1$. (gcd = greatest common divisor)
Prove that the order of $G$ is a prime number and the group is cycle.
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