Residual π-Finiteness of Tubular Groups

IF 0.4 3区数学 Q4 LOGIC

Algebra and Logic Pub Date : 2024-12-21 DOI:10.1007/s10469-024-09768-9

F. A. Dudkin, A. V. Usikov

引用次数: 0

Abstract

A finitely generated group G, which acts on a tree so that all edge stabilizers are infinite cyclic groups and all vertex stabilizers are free rank 2 Abelian groups, is called a tubular group. Every tubular group is isomorphic to the fundamental group π₁(𝒢) of a suitable finite graph 𝒢 of groups. We prove a criterion for residual π-finiteness of tubular groups presented by trees of groups. Also we state a criterion for residual p-finiteness of tubular groups whose corresponding graph contains one edge outside a maximal subtree.

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管群的残差π有限性

一个有限生成的群G作用于一棵树上，使得所有边稳定子都是无限循环群，所有顶点稳定子都是自由2秩阿贝尔群，我们称之为管群。每一个管状群与合适的群的有限图𝒢的基群π1（𝒢）是同构的。证明了由群树表示的管群的残差π有限的一个判据。并给出了管群的残差p有限性判据，其对应图在极大子树外有一条边。

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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来源期刊

Algebra and Logic 数学-数学

CiteScore

1.10

自引率

20.00%

发文量

审稿时长

>12 weeks

期刊介绍： This bimonthly journal publishes results of the latest research in the areas of modern general algebra and of logic considered primarily from an algebraic viewpoint. The algebraic papers, constituting the major part of the contents, are concerned with studies in such fields as ordered, almost torsion-free, nilpotent, and metabelian groups; isomorphism rings; Lie algebras; Frattini subgroups; and clusters of algebras. In the area of logic, the periodical covers such topics as hierarchical sets, logical automata, and recursive functions. Algebra and Logic is a translation of ALGEBRA I LOGIKA, a publication of the Siberian Fund for Algebra and Logic and the Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences. All articles are peer-reviewed.