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<cfResPublDate>2012-07-02</cfResPublDate>
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<cfIssue>2</cfIssue>
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<cfTitle cfLangCode='EN' cfTrans='o'>Construction of subdirectly irreducible SQS-skeins of cardinality n2m</cfTitle>
<cfKeyw cfLangCode='EN' cfTrans='o'>Steiner triple system; Steiner loop; sloop; subdirectly irreducible sloop</cfKeyw>
<cfAbstr cfLangCode='EN' cfTrans='o'>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).</cfAbstr>
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