On an Inequality of Dimension-like Invariants for Finite Groups

Abstract

In this paper, we introduce several notions of "dimension" of a finite group, involving sizes of generating sets and certain configurations of maximal subgroups. We focus on the inequality $m(G)\le \mathrm{MaxDim}(G)$, giving a family of examples where the inequality is strict, and showing that equality holds if $G$ is supersolvable.

arXiv comment20 pages

Cited by in corpus (6)

• The Replacement Property of PSL$(2,p)$ and PSL$(2,p^2)$
• On the Intersection Numbers of Finite Groups
• On the minimal dimension of a finite simple group (with an appendix by T.C. Burness and R.M. Guralnick)
• Maximal subgroups of finite soluble groups in general position
• On Behaviors of Maximal Dimension
• Irredundant generating sets and dimension-like invariants of the finite group