On the semidistributivity of elements in weak congruence lattices of algebras and groups

• Autores: Gábor Czédli, Branimir Seselja, Andreja Tepavcevic
• Localización: Algebra universalis, ISSN 0002-5240, Vol. 58, Nº. 3, 2008, págs. 349-355
• Idioma: inglés
• DOI: 10.1007/s00012-008-2076-y
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• Resumen

  • Weak congruence lattices and semidistributive congruence lattices are both recent topics in universal algebra. This motivates the main result of the present paper, which asserts that a finite group G is a Dedekind group if and only if the diagonal relation is a join-semidistributive element in the lattice of weak congruences of G. A variant in terms of subgroups rather than weak congruences is also given. It is pointed out that no similar result is valid for rings. An open problem and some results on the join-semidistributivity of weak congruence lattices are also included.