TITLE: Group of order 15 is abelian
QUESTION [45 upvotes]: How do I prove that a group of order 15 is abelian?
Is there any general strategy to prove that a group of particular order (composite order) is abelian?

REPLY [13 votes]: In addition to the answers of Hans and Pete: it is well-known that if $n$ is a natural number, there is only one group of order $n$ if and only if $\gcd(n,\phi(n))=1$. Here $\phi$ is the Euler totient function. For $n=15$ this applies.