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# Cyclic Groups of Order Product of Two Distinct Primes

ABSALG-RT1IXI

In which of the following cases is the group $G$ guaranteed to be cyclic?

A

$G$ has order $pq$, where $p, q$ are prime numbers.

B

$G$ has order $pq$, where $p, q$ are distinct prime numbers.

C

$G$ has order $pq$, where $p, q$ are distinct prime numbers with $p$ not dividing $q-1$.

D

$G$ has order $pq$, where $p, q$ are distinct prime numbers and $G$ contains subgroups of order $p$ and $q$.