University of IsfahanInternational Journal of Group Theory2251-765020220523Irredundant families of maximal subgroups of finite solvable groups2662010.22108/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_3b319d8f75c300a312065eb5e58ce65d.pdf