Abstract
Each finite, sharply multiply transitive group of permutations of transitivity t and degree d (2 ≤ t < d) leads to a partial algebra, called a discrete prototype, whose group of automorphisms contain the given group. Each discrete prototype creates a class of partial algebras, each with d operations of t arguments. Each Steiner system S(t, d, v) of the given type is formed from an algebra in this class. Often the partial algebras extend to total algebras and the class of them is definable by identities.
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Knoebel, A. Algebras That Represent Steiner Systems Through Permutation Groups. Ann. Comb. 18, 327–340 (2014). https://doi.org/10.1007/s00026-014-0225-x
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DOI: https://doi.org/10.1007/s00026-014-0225-x