On k-geodetic graphs and groups

IF 0.5 2区数学 Q3 MATHEMATICS

International Journal of Algebra and Computation Pub Date : 2022-11-24 DOI:10.1142/s0218196723500534

M. Elder, Adam Piggott, K. Townsend

引用次数: 1

Abstract

We call a graph $k$-geodetic, for some $k\geq 1$, if it is connected and between any two vertices there are at most $k$ geodesics. It is shown that any hyperbolic group with a $k$-geodetic Cayley graph is virtually-free. Furthermore, in such a group the centraliser of any infinite order element is an infinite cyclic group. These results were known previously only in the case that $k=1$. A key tool used to develop the theorem is a new graph theoretic result concerning ``ladder-like structures'' in a $k$-geodetic graph.

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关于k-大地测量图和群

我们称一个图为$k$-大地测量，对于一些$k\geq1$，如果它是连通的，并且在任何两个顶点之间最多有$k$测地线。证明了具有$k$-大地Cayley图的任何双曲群实际上是自由的。此外，在这样的群中，任何无限阶元素的中心都是无限循环群。这些结果以前只有在$k=1$的情况下才知道。用于发展该定理的一个关键工具是关于$k$-大地图中“梯形结构”的一个新的图论结果。

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

International Journal of Algebra and Computation 数学-数学

CiteScore

1.20

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The International Journal of Algebra and Computation publishes high quality original research papers in combinatorial, algorithmic and computational aspects of algebra (including combinatorial and geometric group theory and semigroup theory, algorithmic aspects of universal algebra, computational and algorithmic commutative algebra, probabilistic models related to algebraic structures, random algebraic structures), and gives a preference to papers in the areas of mathematics represented by the editorial board.