A straightforward solution to the Burnside Problem

TL;DR

This paper provides a direct solution to the Burnside Problem for 2-generator groups of prime-power exponent, avoiding the use of induced maps and utilizing a surjective map to a solvable group.

Contribution

It introduces a new straightforward method for solving the Burnside Problem for specific groups, bypassing previous reliance on induced maps.

Findings

Constructed a surjective map from a free group to a solvable group

Proved the Burnside group is an image of the constructed group

Utilized Theorem B from prior work to support the proof

Abstract

We present a solution to the Burnside Problem for 2 generator groups of prime-power exponent that does not rely on induced maps as in [2]. As before, we construct a surjective map of a rank 2 free group to a solvable group G and finish by showing that the Burnside group is an image of G. Theorem B in the paper with H. A. Heilbronn and H. Y. Mochizuki [9] is indispensable in the proof.