Existence of nilpotent \(SQS\)-skeins of class \(n\)

We construct nilpotent \(SQS\)-skeins of class \(n\), for any positive integer \(n\). These \(SQS\)-skeins are all subdirectly irreducible algebras. The nilpotent \(SQS\)-skeins of class \(n\), which are constructed in this paper, are also solvable of order \( \leq \frac{n+1}{2} \) if \(n\) is odd, and of order \(\leq 1+\frac{1}{2}n\) if \(n\) is even.