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 SM ISO690:2012ELZAYAT, Enas-M.. Construction of subdirectly irreducible SQS-skeins of cardinality n2m. In: Quasigroups and Related Systems, 2012, vol. 20, nr. 2(28), pp. 211-218. ISSN 1561-2848. |
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 Quasigroups and Related Systems |
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| Volumul 20, Numărul 2(28) / 2012 / ISSN 1561-2848 | ||||||
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| Pag. 211-218 | ||||||
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We give a construction for subdirectly irreducible SQS-skeins of cardinality n2m having a monolith with a congruence class of cardinality 2m for each integer m > 2. Moreover, the homomorphic image of the constructed SQS-skein modulo its atom is isomorphic to the initial SQS-skein. Consequently, we will construct an SK(n2m) with a derived SL(n2m) such that SK(n2m) and SL(n2m) are subdirectly irreducible and have the same congruence lattice.
Also, we may construct an SK(n2m) with a derived SL(n2m) in which the congruence lattice of SK(n2m) is a proper sublattice of the congruence lattice of SK(n2m). |
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| Cuvinte-cheie Steiner triple system, Steiner loop, sloop, subdirectly irreducible sloop |
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Dublin Core Export
<?xml version='1.0' encoding='utf-8'?> <oai_dc:dc xmlns:dc='http://purl.org/dc/elements/1.1/' xmlns:oai_dc='http://www.openarchives.org/OAI/2.0/oai_dc/' xmlns:xsi='http://www.w3.org/2001/XMLSchema-instance' xsi:schemaLocation='http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd'> <dc:creator>Elzayat, E.A.</dc:creator> <dc:date>2012-07-02</dc:date> <dc:description xml:lang='en'>We give a construction for subdirectly irreducible SQS-skeins of cardinality n2m having a monolith with a congruence class of cardinality 2m for each integer m > 2. Moreover, the homomorphic image of the constructed SQS-skein modulo its atom is isomorphic to the initial SQS-skein. Consequently, we will construct an SK(n2m) with a derived SL(n2m) such that SK(n2m) and SL(n2m) are subdirectly irreducible and have the same congruence lattice. Also, we may construct an SK(n2m) with a derived SL(n2m) in which the congruence lattice of SK(n2m) is a proper sublattice of the congruence lattice of SK(n2m).</dc:description> <dc:source>Quasigroups and Related Systems 28 (2) 211-218</dc:source> <dc:subject>Steiner triple system</dc:subject> <dc:subject>Steiner loop</dc:subject> <dc:subject>sloop</dc:subject> <dc:subject>subdirectly irreducible sloop</dc:subject> <dc:title>Construction of subdirectly irreducible SQS-skeins of cardinality n2m</dc:title> <dc:type>info:eu-repo/semantics/article</dc:type> </oai_dc:dc>
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