## Three fantastic groups

About three interesting groups: Nichols-Rubik cube, Grigorchuk group, Gupta-Sidki group.

About three interesting groups: Nichols-Rubik cube, Grigorchuk group, Gupta-Sidki group.

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.

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 …

A bit more update on the project of natural spaces. Which groups are natural, which metric spaces are natural, which graphs are natural?

Is the dyadic group of integers natural in the sense that there is a metric space which forces the group structure on it?