الفهرس 
SummaryOnly 14 pages are availabe for public view
 |  | from | 129 |  |  |
| | | from | 129 | | |
Abstract
In this thesis we study the relation between Steiner loops and the other algebras having only one binary operation and we study the relation between Steiner loops and Steiner triple systems. Also we study the properties of SQS-skeins and its relation with Steiner quadruple systems and show that the algebra of sloops is a derived algebra of the algebra of SQS-skeins. We introduce the classification of sloops and SQS-skeins of cardinality 16 according to the shape of them congruence lattice. We discuss the classification for subdirectly irreducible sloops of cardinality 32 which coincides with the classification for subdirectly irreducible SQS-skein of cardinality 32 and unify the classifications for both in one table including the algebraic and combinatoric properties for each class. We give recursive construction theorems as n 2n for subdirectly irreducible SL(2n)s and SK(2n)s, for each possible number n. Also we construct an SK(2n) that has a derived SL(2n) such that SK(2n) and SL(2n) are subdirectly irreducible and have the same congruence lattice. Moreover, we construct an SK(2n) with a derived SL(2n) in which the congruence lattice of SK(2n) is a proper sublattice of the congruence lattice of SL(2n). Finally, we give a construction for subdirectly irreducible SL(n2m) having a monolith with a congruence class of cardinality 2m for each integer m ≥ 2. This construction supplies us with the fact that each sloop is isomorphic to the homomorphic image of the constructed subdirectly irreducible sloop over its monolith.