Group Signature Formulas Constructed from Graphs

IF 0.4 3区数学 Q4 LOGIC

Algebra and Logic Pub Date : 2022-10-14 DOI:10.1007/s10469-022-09682-y

E. I. Timoshenko

引用次数: 0

Abstract

Given a finite undirected graph Γ without loops, we define a sentence Φ(Γ) of group theory. A sequence of graphs Γ_i is used to obtain a sequence of sentences Φ(Γ_i). These are employed to determine the Γ-dimension of a group and to study properties of the dimension. Under certain restrictions on a group, the known centralizer dimension is the Γ-dimension for some sequence of graphs. We mostly focus on dimensions defined by using linear graphs and cycles. Dimensions for a number of partially commutative metabelian groups are computed.

查看原文本刊更多论文

由图构造的群签名公式

给定一个不带环的有限无向图Γ，我们定义了群论的一个句子Φ（Γ）。图Γi的序列用于获得句子Φ（Γi）的序列。这些方法用于确定群的Γ-维，并研究该维的性质。在群上的某些限制条件下，已知的中心化子维数是某些图序列的Γ-维数。我们主要关注通过使用线性图和循环定义的维度。计算了一组部分可交换的偏李群的维数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.