• Corpus ID: 119588940

# On an Inequality of Dimension-like Invariants for Finite Groups

@article{Fernando2015OnAI,
title={On an Inequality of Dimension-like Invariants for Finite Groups},
author={Ravi Fernando},
journal={arXiv: Group Theory},
year={2015}
}
• Ravi Fernando
• Published 2 February 2015
• Mathematics
• arXiv: Group Theory
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 $m(G) \leq \mathrm{MaxDim}(G)$, giving a family of examples where the inequality is strict, and showing that equality holds if $G$ is supersolvable.
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Given a finite group G, an independent set S in G is a set where no element of S can be written as a word in the other elements of S. A minimax set is an independent generating set for G of largest
Preface In chapter 1 we introduce the idea of a supersoluble group and we investigate its connexion with other similar concepts such as solubility and nilpotency. In chapter 2 we look at supersoluble