Nitpicky Sylow Subgroup Question Would we call the trivial subgroup of a finite group $G$ a Sylow-$p$ subgroup if $p \nmid |G|$? Or do we just only look at Sylow-$p$ subgroups as being at least the size $p$ (knowing that a Sylow-$p$ subgroup is a subgroup of $G$ with order $p^k$ where $k$ is the largest power of $p$ that has $p^k \mid |G|$)?

I believe it is customary among most authors to take only primes that divide the group's order. Now, if you're doing some calculations over a large or infinite number of primes then you could always define a Sylow subgroup of a prime not dividing the group's order as the trivial subgroup.
