On a class of groups with given cofactors of maximal subgroups

The paper is devoted to the solution of the general problem of describing finite solvable groups all of whose cofactors of maximal subgroups belong to a given class \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathfrak{X} $$\end{document} of groups. The cases in which \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathfrak{X} $$\end{document} is a homomorph, a Schunk class, and a formation are treated separately. The approach suggested here is related to the construction of a local Schunk class defined by using a constant group function.