Construction of nilpotent sloops of class n Original Research Article

We give in this paper a construction of nilpotent sloops of class n; for any positive integer n. We have the result, that for any n there is an SQS-skein of nilpotence class n which has a derived sloop that is also of nilpotence class n. Guelzow (1993) shows that there is a nilpotent SQS-skeins, all its derived sloops are Boolean. From another direction, we show that the constructed nilpotent sloop can be embedded as a derived sloop of a nilpotent SQS-skein, both are of the same class n. The constructed nilpotent SQS-skein and its derived nilpotent sloop, both have the same congruence lattice and the same central series.