具有一致几乎平商的剩余有限群

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics Pub Date : 2025-09-10 DOI:10.1016/j.aim.2025.110495

David Guo, Matthew Tointon

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引用次数: 0

摘要

我们证明了如果一个多环群的所有有限余集空间的直径在其大小上均以一个多项式为界，那么这个群是几乎幂零的。在有限商群的直径在其大小上有一个多项式有界的较弱假设下，我们对有限生成的剩余无扭转幂零群得到了同样的结论。这扩展了Khukhro和Valette的工作。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Residually finite groups with uniformly almost flat quotients

We show that if all the finite coset spaces of a polycyclic group have diameter bounded uniformly below by a polynomial in their size then the group is virtually nilpotent. We obtain the same conclusion for a finitely generated residually torsion-free nilpotent group under the weaker assumption that the finite quotient groups have diameter bounded uniformly below by a polynomial in their size. This extends work of Khukhro and Valette.

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来源期刊

Advances in Mathematics 数学-数学

CiteScore

2.80

自引率

5.90%

发文量

497

审稿时长

7.5 months

期刊介绍： Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.