Uncountably many $2$-generated just-infinite branch pro-$2$ groups

TL;DR

This paper proves the existence of uncountably many non-isomorphic 2-generated just-infinite branch pro-2 groups, expanding the understanding of their diversity and structure.

Contribution

It establishes that there are continuum many such groups, demonstrating a vast diversity in their classification.

Findings

Existence of 2^{}} non-isomorphic 2-generated just-infinite branch pro-2 groups

The result shows a rich and uncountably infinite variety of these groups

Advances the classification of pro-2 groups by revealing their large diversity.

Abstract

The aim of this note is to prove that there are $2^{\aleph_0}$ non-isomoprhic 2-generated just-infinite branch pro-$2$ groups.