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 SM ISO690:2012ARMANIOUS, Magdi, ELZAYAT, Enas-M.. Subdirectly irreducible sloops and SQS-skeins
. In: Quasigroups and Related Systems, 2007, vol. 15, nr. 2(18), pp. 233-250. ISSN 1561-2848. |
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| Quasigroups and Related Systems | ||||||
| Volumul 15, Numărul 2(18) / 2007 / ISSN 1561-2848 | ||||||
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| Pag. 233-250 | ||||||
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It was shown in [2] that there is 8 classes of nonsimple subdirectly irre-
ducible SQS-skeins of cardinality 32 (SK(32)s). Now, we present the same
classi cation for sloops of cardinality 32 (SL(32)s) and unify this classi-
cation for both SL(32)s and SK(32)s in one table. Next, some recur-
sive 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 subdi-
rectly 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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| Cuvinte-cheie Steiner triple system, Steiner loops, Steiner quadruple system, SQS-skein |
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