广义baumslag -孤子群普遍等价于树群

IF 0.6 3区数学 Q4 LOGIC

Algebra and Logic Pub Date : 2025-08-26 DOI:10.1007/s10469-025-09790-5

F. A. Dudkin

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引用次数: 0

摘要

作用于树上使所有顶点和边稳定子都是无限循环群的有限生成群称为广义Baumslag-Solitar群（GBS群）。每一个GBS群都是一个合适的标记图的基本群π1(如果是一个标记树，那么我们称π1（）为一个GBS群树。已知与树群同构的GBS群本身就是树群。证明了与树群普遍等价的GBS群不一定是树群。此外，我们还给出了与树群普遍等价的所有GBS群的描述。

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Generalized Baumslag–Solitar Groups Universally Equivalent to Tree Groups

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Generalized Baumslag–Solitar Groups Universally Equivalent to Tree Groups

A finitely generated group that acts on a tree so that all vertex and edge stabilizers are infinite cyclic groups is called a generalized Baumslag–Solitar group (GBS group). Every GBS group is the fundamental group π₁(𝔸) of a suitable labeled graph 𝔸. If 𝔸 is a labeled tree, then we call π₁(𝔸) a tree GBS group. It is known that GBS groups isomorphic to tree groups are themselves tree groups. It is shown that GBS groups universally equivalent to tree groups do not have to be tree groups. Moreover, we give a description of all GBS groups that are universally equivalent to tree groups.

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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.