Geometry of Generated Groups with Metrics Induced by Their Cayley Color Graphs
© 2019 Teerapong Suksumran, published by Sciendo 2019. Let G be a group and let S be a generating set of G. In this article,we introduce a metric dC on G with respect to S, called the cardinal metric.We then compare geometric structures of (G, dC) and (G, dW), where dW denotes the word metric. In pa...
Saved in:
| Main Author: | |
|---|---|
| Format: | Journal |
| Published: |
2019
|
| Subjects: | |
| Online Access: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85063507354&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/65685 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Chiang Mai University |
| Summary: | © 2019 Teerapong Suksumran, published by Sciendo 2019. Let G be a group and let S be a generating set of G. In this article,we introduce a metric dC on G with respect to S, called the cardinal metric.We then compare geometric structures of (G, dC) and (G, dW), where dW denotes the word metric. In particular, we prove that if S is finite, then (G, dC) and (G, dW) are not quasiisometric in the case when (G, dW) has infinite diameter and they are bi-Lipschitz equivalent otherwise. We also give an alternative description of cardinal metrics by using Cayley color graphs. It turns out that colorpermuting and color-preserving automorphisms of Cayley digraphs are isometries with respect to cardinal metrics. |
|---|