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 SM ISO690:2012PIORO, Konrad. On finite quasigroups whose subquasigroup lattices are distributive. In: Quasigroups and Related Systems, 2007, vol. 15, nr. 2(18), pp. 309-316. ISSN 1561-2848. |
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| Quasigroups and Related Systems | ||||||
| Volumul 15, Numărul 2(18) / 2007 / ISSN 1561-2848 | ||||||
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| Pag. 309-316 | ||||||
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We prove that if the subquasigroup lattice of a nite quasigroup Q is dis-
tributive, then Q is cyclic (i.e., Q is generated by one element) and also,
each of its subquasigroups is also cyclic. Finally, we give examples which
show that the inverse implication does not hold.
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| Cuvinte-cheie quasigroup, cyclic quasigroup, subquasigroup, subquasigroup lattice, distributive lattice |
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