# Irredundant families of maximal subgroups of finite solvable groups

Document Type : Ischia Group Theory 2020/2021

Author

Faculty of Mathematics, University of Bialystok, Ciolkowskiego 1M, 15-245 Bialystok, Poland

Abstract

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.

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