No abstract

In the paper, a Frattini-like subgroup associated with a class X of simple groups is introduced and analysed. The corresponding X-saturated formations are exactly the X-local ones introduced by Förster. Our techniques are also very useful to highlight the properties and behaviour of ω-local formations. In fact, extensions and improvements of several results of Shemetkov are natural consequences of our study.

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An easy-to-use procedure is presented for improving theε-constraint method for computing the efficient frontier of the portfolio selection problem endowed with additional cardinality and semicontinuous variable constraints. The proposed method provides not only a numerical plotting of the frontier but also an analytical description of it, including the explicit equations of the arcs of parabola it comprises and the change points between them. This information is useful for performing a sensitivity analysis as well as for providing additional criteria to the investor in order to select an efficient portfolio. Computational results are provided to test the efficiency of the algorithm and to illustrate its applications. The procedure has been implemented in Mathematica.

It is shown in this paper that if X is a class of simple groups such that TT(JE) = char X, the 3E-saturated formation f) generated by a finite group cannot be expressed as the Gaschiitz product J? o