IRREDUNDANT FAMILIES OF MAXIMAL SUBGROUPS OF FINITE SOLVABLE GROUPS

Let M be a family of maximal subgroups of a group G. We say that M is irredundant if its intersection is not equal to the intersection of any proper subfamily of M. The maximal dimension of G is the maximal size of an irredundant family of maximal subgroups of G. In this paper we study a class of solvable groups, called M-groups, in which the maximal dimension has properties analogous to that of the dimension of a vector space such as the span property, the extension property and the basis exchange property.