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The lattice of Fitting classes which are right extensible by soluble groups.

M.J. Iranzo, Julio P. Lafuente, F. Pérez-Monasor (2005)

Publicacions Matemàtiques

In this paper we study the set of Fitting classes which are right extensible by soluble groups ordered by the inclusion relation. The consideration of the associated lattices gives rise to new Fitting classes and it allows to obtain some injectivity criteria for general Fitting classes.

The lattice of ideals of a numerical semigroup and its Frobenius restricted variety associated

Maria Angeles Moreno-Frías, José Carlos Rosales (2024)

Mathematica Bohemica

Let Δ be a numerical semigroup. In this work we show that 𝒥 ( Δ ) = { I { 0 } : I is an ideal of Δ } is a distributive lattice, which in addition is a Frobenius restricted variety. We give an algorithm which allows us to compute the set 𝒥 a ( Δ ) = { S 𝒥 ( Δ ) : max ( Δ S ) = a } for a given a Δ . As a consequence, we obtain another algorithm that computes all the elements of 𝒥 ( Δ ) with a fixed genus.

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