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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.
Let be a numerical semigroup. In this work we show that is a distributive lattice, which in addition is a Frobenius restricted variety. We give an algorithm which allows us to compute the set for a given As a consequence, we obtain another algorithm that computes all the elements of with a fixed genus.
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