The lattice of Fitting classes which are right extensible by soluble groups. (Q2574020)

All groups considered in the paper are assumed to be finite. The product of two classes of groups \(\mathfrak F\) and \(\mathfrak G\) is the class \(\mathfrak{FG}\) of the groups \(G\) which have a normal subgroup \(N\) such that \(N\in\mathfrak F\) and \(G/N\in\mathfrak G\). Let \(\mathcal T\) be the set of all Fitting classes \(\mathfrak T\) such that \(\mathfrak T=\mathfrak{TS}\), where \(\mathfrak S\) is the class of soluble groups. The paper studies the set \(\mathcal T\) 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.