التفاصيل البيبلوغرافية
| العنوان: |
Generalized torsion elements in infinite groups |
| المؤلفون: |
Bastos, Raimundo, Mendonça, Luis |
| سنة النشر: |
2024 |
| المجموعة: |
Mathematics |
| مصطلحات موضوعية: |
Mathematics - Group Theory |
| الوصف: |
A group element is called generalized torsion if a finite product of its conjugates is equal to the identity. We show that in a finitely generated abelian-by-finite group, an element is generalized torsion if and only if its image in the abelianization is torsion. We also prove a quantitative version with sharp bounds to the generalized exponent of these groups. In particular, we provide many examples of finitely presentable torsion-free groups in which all elements are generalized torsion. We also discuss positive generalized identities in abelian-by-finite groups and related classes. |
| نوع الوثيقة: |
Working Paper |
| URL الوصول: |
http://arxiv.org/abs/2411.17918 |
| رقم الانضمام: |
edsarx.2411.17918 |
| قاعدة البيانات: |
arXiv |