Finitely generated subgroups of algebraic elements of plane Cremona groups are bounded

被引：1

作者：

Lonjou, Anne ^{[1
,2
]}

Przytycki, Piotr ^{[3
]}

Urech, Christian ^{[4
]}

机构：

[1] Univ Basque Country UPV EHU, Dept Math, Sarriena S-N, Leioa 48940, Bizkaia, Spain

[2] Basque Fdn Sci, IKERBASQUE, Bilbao, Spain

[3] McGill Univ, Dept Math & Stat, Burnside Hall,805 Sherbrooke St West, Montreal, PQ H3A 0B9, Canada

[4] Swiss Fed Inst Technol, Dept Math, Ramistr 101, CH-8092 Zurich, Switzerland

来源：

JOURNAL DE L ECOLE POLYTECHNIQUE-MATHEMATIQUES | 2024年 / 11卷

基金：

加拿大自然科学与工程研究理事会; 欧盟地平线“2020”;

关键词：

Cremona group; algebraic elements; locally elliptic actions; degree growth; SURFACES;

D O I：

10.5802/jep.271

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that any finitely generated subgroup of the plane Cremona group consisting only of algebraic elements is of bounded degree. This follows from a more general result on 'decent' actions on infinite restricted products. We apply our results to describe the degree growth of finitely generated subgroups of the plane Cremona group.

引用

页数：19

共 50 条

[31] FINITELY GENERATED ABELIAN GROUPS AS UNIONS OF PROPER SUBGROUPS
ROSENFELD, A
AMERICAN MATHEMATICAL MONTHLY, 1963, 70 (10): : 1070 - &
[32] Abelian subgroups of finitely generated Kleinian groups are separable
Allman, ES
Hamilton, E
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1999, 31 : 163 - 172
[33] Free subgroups of finitely generated free profinite groups
Shusterman, Mark
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2016, 93 : 361 - 378
[34] On subgroups of finite index in positively finitely generated groups
Nikolov, N
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2005, 37 : 873 - 877
[35] On the intersection of finitely generated subgroups in free products of groups
Ivanov, SV
INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 1999, 9 (05) : 521 - 528
[36] Groups with subnormality for all subgroups that are not finitely generated.
Heineken, H
Kurdachenko, LA
ANNALI DI MATEMATICA PURA ED APPLICATA, 1995, 169 : 203 - 232
[37] BOUNDED ELEMENTS OF LINEAR ALGEBRAIC GROUPS
SIT, KYC
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 209 (AUG) : 185 - 198
[38] ALGEBRAIC CONVERGENCE OF FINITELY GENERATED KLEINIAN-GROUPS
JORGENSEN, T
KLEIN, P
QUARTERLY JOURNAL OF MATHEMATICS, 1982, 33 (131): : 325 - 332
[39] Finitely generated subgroups of free profinite groups and of some Galois groups
Mel'nikov, OV
MATHEMATICAL NOTES, 1998, 64 (1-2) : 82 - 91
[40] Finitely generated subgroups of free profinite groups and of some Galois groups
O. V. Mel'nikov
Mathematical Notes, 1998, 64 : 82 - 91

← 1 2 3 4 5 →