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

被引：6

作者：

Bubboloni, Daniela ^{[1
]}

Praeger, Cheryl E. ^{[2
]}

Spiga, Pablo ^{[3
]}

机构：

[1] Univ Firenze, Dipartimento Matemat & Informat, Viale Morgagni 67-A, I-50134 Florence, Italy

[2] Univ Western Australia, Sch Phys Math & Comp, Ctr Math Symmetry & Computat, Crawley, WA 6009, Australia

[3] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, Via Cozzi 55, I-20125 Milan, Italy

来源：

MONATSHEFTE FUR MATHEMATIK | 2020年 / 191卷 / 02期

关键词：

Symmetric groups; Conjugacy classes; Normal coverings; Partitions; FINITE; POLYNOMIALS;

D O I：

10.1007/s00605-019-01287-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The normal covering number gamma(G) 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 gamma(Sn) when n is even, and for gamma(An), when n is odd.

引用

页码：229 / 247

页数：19

共 16 条

[1]

Andrews G.E., 1976, ENCY MATH ITS APPL

[2] Polynomials with roots mod p for all primes p [J].

Brandl, R ;

Bubboloni, D ;

Hupp, I .

JOURNAL OF GROUP THEORY, 2001, 4 (02) :233-239

[3] Normal coverings of linear groups [J].

Britnell, John R. ;

Maroti, Attila .

ALGEBRA & NUMBER THEORY, 2013, 7 (09) :2085-2102

[4]

Bubboloni D, 2016, MANUSCRIPTA MATH, V151, P477, DOI 10.1007/s00229-016-0848-9

[5]

Bubboloni D, 2014, INT J GROUP THEORY, V3, P57

[6] Normal coverings and pairwise generation of finite alternating and symmetric groups [J].

Bubboloni, Daniela ;

Praeger, Cheryl E. ;

Spiga, Pablo .

JOURNAL OF ALGEBRA, 2013, 390 :199-215

[7] Compositions of n satisfying some coprimality conditions [J].

Bubboloni, Daniela ;

Luca, Florian ;

Spiga, Pablo .

JOURNAL OF NUMBER THEORY, 2012, 132 (12) :2922-2946

[8] Normal coverings of finite symmetric and alternating groups [J].

Bubboloni, Daniela ;

Praeger, Cheryl E. .

JOURNAL OF COMBINATORIAL THEORY SERIES A, 2011, 118 (07) :2000-2024

[9] On the Diophantine equation xm-1/x-1 = yn-1/y-1 [J].

Bugeaud, Y ;

Shorey, TN .

PACIFIC JOURNAL OF MATHEMATICS, 2002, 207 (01) :61-75

[10]

El Bachraoui M, 2008, FIBONACCI QUART, V46-47, P341

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