Definition of $k$-transposition group

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In A monster tale: a review on Borcherds’ proof of monstrous moonshine conjecture, a $k$-transposition group is defined as follows.

Recall that a $k$-transposition group $G$ is one generated by a conjugacy class $K$ of involutions, where the product $gh$ of any two elements of $K$ has order at most $k$.

I am trying to understand this. Does it mean that $G$ is generated by a multiplication of $k$ transpositions? For example: is $\langle (1, 2) (3, 4) (5, 6)\rangle$ a transposition group?