Generalized torsion elements in groups

被引：0

作者：

Bastos, Raimundo ^{[1
]}

Schneider, Csaba ^{[2
]}

Silveira, Danilo ^{[3
]}

机构：

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

[2] Univ Fed Minas Gerais, Dept Matemat, BR-31270901 Belo Horizonte, MG, Brazil

[3] Univ Fed Ouro Preto, Dept Ciencias Exatas & Aplicadas, BR-35931008 Ouro Preto, MG, Brazil

来源：

ARCHIV DER MATHEMATIK | 2024年 / 122卷 / 02期

关键词：

Generalized torsion; Torsion; Generalized order; Generalized exponent; Character theory; CONJUGACY CLASSES;

D O I：

10.1007/s00013-023-01931-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A group element is called a generalized torsion element if a finite product of its conjugates is equal to the identity. We prove that in a nilpotent or FC-group, the generalized torsion elements are all torsion elements. Moreover, we compute the generalized order of an element in a finite group G using its character table.

引用

页码：121 / 131

页数：11

共 18 条

[1] ARAD Z, 1985, LECT NOTES MATH, V1112, P6
[2] Bludov V. V., 1972, Algebra i Logika, V11, P736
[3] Conway J.H., 1999, SPHERE PACKINGS LATT, V3rd
[4] Gorakov JM., 1967, ALGEBRA LOGIKA SEMIN, V6, P5
[5] Gorjuskin AP., 1973, SIBIRSK MAT, V14, P204
[6] Huppert B., 1967, ENDLICHE GRUPPEN
[7] Ito T., 2023, ARXIV
[8] Generalized torsion for hyperbolic 3-manifold groups with arbitrary large rank
Ito, Tetsuya
Motegi, Kimihiko
Teragaito, Masakazu
[J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2023, 55 (03) : 1203 - 1209
[9] Generalized torsion and Dehn filling
Ito, Tetsuya
Motegi, Kimihiko
Teragaito, Masakazu
[J]. TOPOLOGY AND ITS APPLICATIONS, 2021, 301
[10] Khukhro E. I., 2022, ARXIV

← 1 2 →