由图构造的群签名公式

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

E. I. Timoshenko

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引用次数: 0

摘要

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。

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Group Signature Formulas Constructed from Graphs

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.

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