The order of the group $G$, meet the following conditions: $1
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.
Prove that G is cyclic if distinct subgroups have coprime orders
1
$\begingroup$
group-theory
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0What do you mean by a neutral number? Since this looks like a homework problem, what have you tried? – 2012-07-16
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0The order of G is not infinite. – 2012-07-16
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1Note that the condition you mention also has to hold when $H_1 = G$ and $H_2$ is any proper subgroup of $G$. What does Lagrange then tell you? – 2012-07-16
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0@Lag: Those are called **natural** numbers, not "neutral" numbers. – 2012-07-16