On an Inequality of Dimension-like Invariants for Finite Groups

Ravi Fernando

On an Inequality of Dimension-like Invariants for Finite Groups

Group Theory 2015-02-03 v1

Authors: Ravi Fernando

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 $m(G) \leq \mathrm{MaxDim}(G)$ , giving a family of examples where the inequality is strict, and showing that equality holds if $G$ is supersolvable.

Keywords

finite groups dimension-like invariants generating sets maximal subgroups supersolvable groups group inequalities

Cite

@article{arxiv.1502.00360,
  title  = {On an Inequality of Dimension-like Invariants for Finite Groups},
  author = {Ravi Fernando},
  journal= {arXiv preprint arXiv:1502.00360},
  year   = {2015}
}

Comments

20 pages

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