%0 Journal Article
%T Irredundant families of maximal subgroups of finite solvable groups
%J International Journal of Group Theory
%I University of Isfahan
%Z 2251-7650
%A Stocka, Agnieszka
%D 2023
%\ 09/01/2023
%V 12
%N 3
%P 163-176
%! Irredundant families of maximal subgroups of finite solvable groups
%K Intersection of maximal subgroups and maximal dimension and finite solvable groups
%R 10.22108/ijgt.2022.130778.1751
%X Let $\mathcal{M}$ 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.
%U https://ijgt.ui.ac.ir/article_26620_64963867053680d71eab444f3ff10382.pdf