On the subgroups and normal subgroups of the group representation of the Cayley tree

TL;DR

This paper characterizes certain normal subgroups and subgroups of specific indices within the group representation of the Cayley tree, advancing understanding of its subgroup structure.

Contribution

It provides a detailed classification of normal subgroups of index 2^s(2n+1) and subgroups of index three in the Cayley tree's group representation.

Findings

Normal subgroups of index 2^s(2n+1) characterized

Subgroups of index three classified

Enhanced understanding of Cayley tree group structure

Abstract

In this paper, we give a characterization of the normal subgroups of index $2^{s}(2n+1),\ s\in\{1,2\},\ n\in \mathbb{N}$ and of the subgroups of index three of the group representation of the Cayley tree.