Three fantastic groups
About three interesting groups: Nichols-Rubik cube, Grigorchuk group, Gupta-Sidki group.
Category: group theory
Cayley, Zig-Zag and Rubik
We continue to look at natural groups.
There is some progress in seeing that the Rubik cube group is natural: semi direct products can be represented by zig-zag products of Cayley graphs.
Group Extensions and Naturalness
A bit about group theory triggered by the observation that some of the non-natural groups are non-simple groups which do not split. The later problem is a central issue in the classification problem of finite groups. While the finite simple groups have been classified in a monster effort and finitalized …
Graphs, Groups and Geometry
A bit more update on the project of natural spaces. Which groups are natural, which metric spaces are natural, which graphs are natural?
Dyadic world
Is the dyadic group of integers natural in the sense that there is a metric space which forces the group structure on it?