In the book Roads to Infinity: The Mathematics of Truth and Proof, the author stated:
For each n, one has the n-string braid group $B_n$, consisting of all the n-string braids under the braid product operation.
I don't understand what this sentence means, because I don't know it means for a braid to be "under" the braid product operation. Google didn't turn up anything, and the context doesn't seem to help. So, what does it mean for an object to be under an operation?