The independence graph of a finite group

被引：0
作者：
Andrea Lucchini
机构：
[1] Università degli Studi di Padova,Dipartimento di Matematica “Tullio Levi
来源：
Monatshefte für Mathematik | 2020年 / 193卷
关键词：
Generating sets; Generating graph; Connectivity; Planarity; Soluble groups; 20D60; 05C25;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Given a finite group G, we denote by Δ(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta (G)$$\end{document} the graph whose vertices are the elements G and where two vertices x and y are adjacent if there exists a minimal generating set of G containing x and y. We prove that Δ(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta (G)$$\end{document} is connected and classify the groups G for which Δ(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta (G)$$\end{document} is a planar graph.
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页码：845 / 856
页数：11
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