The question came from an example on the book "Contemporary Abstract Algebra" (9th Edition) in page 203.The orginal problem is to prove that every group of order 35 is cyclic.I wondered if there are more groups of order $pq$ is cyclic.And what's the requirements of $p$ and $q$
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This answers your question, see hmmmm's answer. – Bowei Tang Jun 01 '24 at 07:09
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There is a cyclic group of order $n$ for every positive integer $n$, – ajotatxe Jun 01 '24 at 07:14
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This has been asked and answered several times at this site. See for example this post, which again is a duplicate of a duplicate. – Dietrich Burde Jun 01 '24 at 10:02