Maximal irredundant families of minimal size in the alternating group

被引：5

作者：

Garonzi, Martino ^{[1
]}

Lucchini, Andrea ^{[2
]}

机构：

[1] Univ Brasilia, Dept Matemat, Campus Univ Darcy Ribeiro, BR-70910900 Brasilia, DF, Brazil

[2] Univ Padua, Dipartimento Matemat Tullio Levi Civita, Via Trieste 63, I-35131 Padua, Italy

来源：

ARCHIV DER MATHEMATIK | 2019年 / 113卷 / 02期

关键词：

Alternating groups; Maximal subgroups; BASE SIZES;

D O I：

10.1007/s00013-019-01331-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a finite group. A family M of maximal subgroups of G is called irredundant if its intersection is not equal to the intersection of any proper subfamily. M is called maximal irredundant if M is irredundant and it is not properly contained in any other irredundant family. We denote by (G) when G is the alternating group on n letters.

引用

页码：119 / 126

页数：8

共 10 条

[1]

[Anonymous], 2017, GAP GROUPS ALG PROGR

[2] On base sizes for algebraic groups [J].

Burness, Timothy C. ;

Guralnick, Robert M. ;

Saxl, Jan .

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2017, 19 (08) :2269-2341

[3] On base sizes for symmetric groups [J].

Burness, Timothy C. ;

Guralnick, Robert M. ;

Saxl, Jan .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2011, 43 :386-391

[4] Base sizes for simple groups and a conjecture of Cameron [J].

Burness, Timothy C. ;

Liebeck, Martin W. ;

Shalev, Aner .

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2009, 98 :116-162

[5]

Cameron P.J., 1999, LONDON MATH SOC STUD

[6]

Fernando R, ARXIV150200360

[7]

Kleidman P., 1990, SUBGROUP STRUCTURE F

[8]

LIEBECK MW, 1985, J LOND MATH SOC, V31, P237

[9] Maximal independent generating sets of the symmetric group [J].

Whiston, J .

JOURNAL OF ALGEBRA, 2000, 232 (01) :255-268

[10]

Wielandt H, 1956, MATH Z, V63, P478

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