Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 41, No. 1, pp. 85-92 (2000)

Modular Elements in Congruence Lattices of $G$-sets

Boris M. Vernikov

Department of Mathematics and Mechanics, Ural State University, Lenina 51, 620083 Ekaterinburg, Russia e-mail:

Abstract: An element $x$ in a lattice $\langle L; \vee,\wedge\rangle$ is called modular\/ if $(x\vee y)\wedge z=(x\wedge z)\vee y$ whenever $y,z\in L$ and $y\le z$. We describe modular elements in congruence lattices of $G$-sets.

Keywords: $G$-set, congruence lattice, modular element in a lattice.

Classification (MSC2000): 08A60, 08A30

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