Groups as automorphisms of dessins d'enfants

被引：0

作者：

Canas, Alejandro ^{[1
]}

Hidalgo, Ruben A. ^{[2
]}

Turiel, Francisco Javier ^{[1
]}

Viruel, Antonio ^{[1
]}

机构：

[1] Univ Malaga, Dept Algebra Geometria & Topol, Malaga, Spain

[2] Univ La Frontera, Dept Matemat & Estadist, Temuco, Chile

来源：

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS | 2022年 / 116卷 / 04期

关键词：

Automorphisms; Dessins d'enfants; ABSOLUTE GALOIS GROUP;

D O I：

10.1007/s13398-022-01285-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is known that every finite group can be represented as the full group of automorphisms of a suitable compact dessin d'enfant. In this paper, we give a constructive and easy proof that the same holds for any countable group by considering non-compact dessins. Moreover, we show that any tame action of a countable group is so realisable.

引用

页数：9

共 15 条

[1] Hyperbolic surfaces with prescribed infinite symmetry groups
Allcock, D
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2006, 134 (10) : 3057 - 3059
[2] [Anonymous], 1980, LECT NOTES
[3] Aougab T., 2021, MATH ANN, V381, P459, DOI DOI 10.1007/S00208-021-02164-Z
[4] ON GALOIS EXTENSIONS OF A MAXIMAL CYCLOTOMIC FIELD
BELYI, GV
[J]. MATHEMATICS OF THE USSR-IZVESTIYA, 1980, 14 (02): : 247 - 256
[5] Bollobas B., 1998, GRAD TEXT M, V184
[6] Girondo E., 2012, London Math. Soc. Student Texts, V79
[7] A note on the action of the absolute Galois group on dessins
Girondo, Ernesto
Gonzalez-Diez, Gabino
[J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2007, 39 : 721 - 723
[8] The absolute Galois group acts faithfully on regular dessins and on Beauville surfaces
Gonzalez-Diez, Gabino
Jaikin-Zapirain, Andrei
[J]. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2015, 111 : 775 - 796
[9] CONFORMAL TRANSFORMATIONS OF RIEMANN SURFACES
GREENBERG, L
[J]. AMERICAN JOURNAL OF MATHEMATICS, 1960, 82 (04) : 749 - 760
[10] Grothendieck A, 1997, GEOMETRIC GALOIS ACT, P5

← 1 2 →