University of IsfahanInternational Journal of Group Theory2251-765012320230901Irredundant families of maximal subgroups of finite solvable groups1631762662010.22108/ijgt.2022.130778.1751ENAgnieszkaStockaFaculty of Mathematics, University of Bialystok, Ciolkowskiego 1M, 15-245 Bialystok, PolandJournal Article20211004Let $\mathcal{M}$ be a family of maximal subgroups of a group $G.$ We say that $\mathcal{M}$ is irredundant if its intersection is not equal to the intersection of any proper subfamily of $\mathcal{M}$. 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 $\mathcal{M}$-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.https://ijgt.ui.ac.ir/article_26620_64963867053680d71eab444f3ff10382.pdf