4. Let p,q,r be three prime numbers. Let G be a group with order $|G| = pqr$. (a) What is the maximum number of subgroups that G could have? Answer: (b) If H is a subgroup of G, list all possible orders of H.
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We have a group G with order |G| = PqT, where P, q, and T are prime numbers. To find the maximum number of subgroups that G could have, we can use the fact that the number of subgroups of a group is equal to the number of divisors of its order. The order of G Show more…
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