On Subdirectly Irreducible Steiner Loops of Cardinality 2n
نویسنده
چکیده
Let L1 be a finite simple sloop of cardinality n or the 8-element sloop. In this paper, we construct a subdirectly irreducible (monolithic) sloop L = 2⊗αL1 of cardinality 2n, for each n ≥ 8, with n ≡ 2 or 4 (mod 6), in which each proper homomorphic image is a Boolean sloop. Quackenbush [12] has proved that the variety V (L1) generated by a finite simple planar sloop L1 covers the smallest nontrivial subvariety (the class of all Boolean sloops). For any finite planar sloop L1, the variety V (L) generated by the constructed sloop L = 2⊗αL1 covers the variety V (L1). MSC 2000: 05B07 (primary); 20N05 (secondary)
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