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Category: <span>group theory</span>
Home Archive for category "group theory"

Category: group theory

Three fantastic groups
group theory

Three fantastic groups

By oliverknill November 19, 2021 November 24, 2021  combinatorial group theory

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

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Cayley, Zig-Zag and Rubik
Graph theory, group theory

Cayley, Zig-Zag and Rubik

By oliverknill November 7, 2021 November 24, 2021  cayley graphs, rubik, zig-zag

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.

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Group Extensions and Naturalness
Graph theory, group theory

Group Extensions and Naturalness

By oliverknill November 4, 2021 November 6, 2021  graphs, group theory

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 …

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Graphs, Groups and Geometry
discrete geometry, Graph theory, group theory

Graphs, Groups and Geometry

By oliverknill October 29, 2021 October 29, 2021  graphs, groups, metric spaces, natural spaces

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

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Dyadic world
arithmetic, group theory

Dyadic world

By oliverknill October 5, 2021 October 5, 2021  dyadic group of integers, 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?

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