Prove that if a group G has no non-trivial subgroups, G is finite and o(G) is a prime number, where o(G) is the order of the group G.(adsbygoogle = window.adsbygoogle || []).push({});

If G is infinite, you can show that there are non trivial subgroups. What remains to prove is that if o(G) is not prime, than there is at least one subgroup H, with o(H) equal to one of the prime divisor of o(G). Any idea?

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# Non trivial subgroups

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