# On the subexponential growth of groups acting on rooted trees

## TL;DR

This paper proves that a broad class of groups acting on a ternary rooted tree exhibit subexponential growth, expanding understanding of their algebraic complexity.

## Contribution

It establishes that many spinal groups on ternary trees have subexponential growth, a significant extension of known growth properties.

## Key findings

- Groups in the studied family are of subexponential growth.
- The result applies to non-torsion groups.
- It broadens the class of groups known to have subexponential growth.

## Abstract

We show that every group in a large family of (not necessarily torsion) spinal groups acting on the ternary rooted tree is of subexponential growth.