A subexponential bound on the cardinality of abelian quotients in finite transitive groups

被引：0

作者：

Lucchini, Andrea ^{[1
]}

Sabatini, Luca ^{[2
]}

Spiga, Pablo ^{[3
]}

机构：

[1] Univ Padua, Dipartimento Matemat Pura & Applicata, Via Trieste 53, I-35121 Padua, Italy

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

[3] Univ Milano Bicocca, Dipartimento Matemat Pura & Applicata, Via Cozzi 55, I-20126 Milan, Italy

来源：

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 2021年 / 53卷 / 06期

关键词：

20B30; 20B35 (primary); PERMUTATION-GROUPS;

D O I：

10.1112/blms.12532

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that, for every transitive permutation group G of degree n > 2, the largest abelian quotient of G has cardinality at most 4n/log2n. This gives a positive answer to a 1989 outstanding question of Laszlo Kovacs and Cheryl Praeger.

引用

页码：1711 / 1716

页数：6

共 10 条

[1] ON ABELIAN QUOTIENTS OF PRIMITIVE GROUPS [J].

ASCHBACHER, M ;

GURALNICK, RM .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1989, 107 (01) :89-95

[2] ON MINIMAL FAITHFUL PERMUTATION REPRESENTATIONS OF FINITE-GROUPS [J].

EASDOWN, D ;

PRAEGER, CE .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1988, 38 (02) :207-220

[3] Bounding the composition length of primitive permutation groups and completely reducible linear groups [J].

Glasby, S. P. ;

Praeger, Cheryl E. ;

Rosa, Kyle ;

Verret, Gabriel .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2018, 98 (03) :557-572

[4] Normalizers of primitive permutation groups [J].

Guralnick, Robert M. ;

Maroti, Attila ;

Pyber, Laszlo .

ADVANCES IN MATHEMATICS, 2017, 310 :1017-1063

[5] FINITE PERMUTATION-GROUPS WITH LARGE ABELIAN QUOTIENTS [J].

KOVACS, LG ;

PRAEGER, CE .

PACIFIC JOURNAL OF MATHEMATICS, 1989, 136 (02) :283-292

[6] Asymptotic results for transitive permutation groups [J].

Lucchini, A ;

Menegazzo, F ;

Morigi, M .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2000, 32 :191-195

[7] Enumerating transitive finite permutation groups [J].

Lucchini, A .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1998, 30 :569-577

[8] THE CONTRIBUTION OF L. G. KOVACS TO THE THEORY OF PERMUTATION GROUPS [J].

Praeger, Cheryl E. ;

Schneider, Csaba .

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2017, 102 (01) :20-33

[9]

PYBER L., 1993, Groups and computation, P197

[10] Minimal generation of transitive permutation groups [J].

Tracey, Gareth M. .

JOURNAL OF ALGEBRA, 2018, 509 :40-100

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