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# Orders of elements and Cyclic Groups

ABSALG-J3QNXB

In which of the following cases MUST the group $G$ be cyclic?

A

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

B

$G$ has order $pq$, where $p, q$ are distinct prime numbers and contains two elements $x,y$ of order $p$ and $q$ respectively.

C

$G$ has order $pq$, where $p, q$ are distinct prime numbers and contains two commuting elements $x,y$ of order $p$ and $q$ respectively.

D

$G/Z(G)$ is cyclic.