Existence of nilpotent $SQS$-skeins of class $n$

Abstract

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 $\le \frac{n+1}{2}$ if $n$ is odd, and of order $\le 1+\frac{1}{2}n$ if $n$ is even.