What is the group $G=\langle a,b \mid ab^2=b^3a,ba^3=a^2b\rangle $

Asked Oct 25 '23 at 23:30

Active Oct 26 '23 at 10:26

Viewed 64 times

I feel that $G$ is infinite, however I don't know how to deal with the relationship $ab^2=b^3a,ba^3=a^2b$

edited Oct 26 '23 at 10:26

Shaun

asked Oct 25 '23 at 23:30

QiFeng233

2

This is a well-known example of a presentation of the trivial group. This has been asked many times before. – Derek Holt Oct 25 '23 at 23:36
2

The center of the cluster seems to be https://math.stackexchange.com/questions/66573/a-particular-two-variable-system-in-a-group – Chris Culter Oct 25 '23 at 23:38
I got that, thanks! – QiFeng233 Oct 26 '23 at 01:04

0 Answers0