**Authors:** M. H. Armanious and E. M. A. Elzayat

### Abstract

It was shown that there is 8 classes of nonsimple subdirectly irreducible SQS-skeins of cardinality 32 (SK(32)s). Now, we present the same classification for sloops of cardinality 32 (SL(32)s) and unify this classification for both SL(32)s and SK(32)s in one table. Next, some recursive construction theorems for subdirectly irreducible SL(2n)s and SK(2n)s which are not necessary to be nilpotent are given. Further, we construct an SK(2n) with a derived SL(2n) such that SK(2n) and SL(2n) are subdirectly irreducible and have the same congruence lattice. We also construct an SK(2n) with a derived SL(2n) such that the congruence lattice of SK(2n) is a proper sublattice of the congruence lattice of SL(2n).

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