On an Inequality of Dimension-like Invariants for Finite Groups

2015/02/02 by Ravi Fernando, Fernando, Ravi · 4 citations
Mathematics · Engineering · #Finite Group Theory Research #graph theory and CDMA systems #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1502.00360

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) ≤ MaxDim(G), giving a family of examples where the inequality is strict, and showing that equality holds if G is supersolvable.

Cited by

• On the minimal dimension of a finite simple group (with an appendix by T.C. Burness and R.M. Guralnick)
• Irredundant generating sets and dimension-like invariants of the finite group
• Maximal subgroups of finite soluble groups in general position
• The Replacement Property of PSL(2,p) and PSL(2,p²)

Related

• On Behaviors of Maximal Dimension
• MaxDim of some simple groups
• Maximal subgroups of finite soluble groups in general position
• A Summary of Known Bounds on the Essential Dimension and Resolvent Degree of Finite Groups
• Maximal intersections in finite groups