Praefrattinigruppen und Matroide. (Prefrattinigroups and matroids)
Author's English summary: For finite, solvable groups G, the set M(G) of all maximal subgroups, together with a natural independence relation, forms a matroid. So all bases have the same length. The intersection over one basis is conjugate to the intersection over any other basis. It turns out, that such intersections are prefrattini subgroups, introduced by W. Gaschütz. So we have a canonical description of these subgroups. We construct all epimorphism invariant conjugation classes of subgroups, such that each subgroup (of the class) is an intersection of maximal subgroups (of G). The prefrattini subgroups build the `smallest' class.
scientific article; zbMATH DE number 4214245