Linear bounds for the normal covering number of the symmetric and alternating groups

被引：0
作者：
Daniela Bubboloni
Cheryl E. Praeger
Pablo Spiga
机构：
[1] University of Firenze,Dipartimento di Matematica e Informatica
[2] The University of Western Australia,Centre for Mathematics of Symmetry and Computation, School of Physics, Mathematics, and Computing
[3] University of Milano-Bicocca,Dipartimento di Matematica e Applicazioni
来源：
Monatshefte für Mathematik | 2020年 / 191卷
关键词：
Symmetric groups; Conjugacy classes; Normal coverings; Partitions; 20B30; 20F05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The normal covering number γ(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma (G)$$\end{document} of a finite, non-cyclic group G is the minimum number of proper subgroups such that each element of G lies in some conjugate of one of these subgroups. We find lower bounds linear in n for γ(Sn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma (S_n)$$\end{document}, when n is even, and for γ(An)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma (A_n)$$\end{document}, when n is odd.
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页码：229 / 247
页数：18
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